{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov switching autoregression models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook provides an example of the use of Markov switching models in statsmodels to replicate a number of results presented in Kim and Nelson (1999). It applies the Hamilton (1989) filter the Kim (1994) smoother.\n",
    "\n",
    "This is tested against the Markov-switching models from E-views 8, which can be found at http://www.eviews.com/EViews8/ev8ecswitch_n.html#MarkovAR or the Markov-switching models of Stata 14 which can be found at http://www.stata.com/manuals14/tsmswitch.pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import requests\n",
    "from io import BytesIO\n",
    "\n",
    "# NBER recessions\n",
    "from pandas_datareader.data import DataReader\n",
    "from datetime import datetime\n",
    "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hamilton (1989) switching model of GNP\n",
    "\n",
    "This replicates Hamilton's (1989) seminal paper introducing Markov-switching models. The model is an autoregressive model of order 4 in which the mean of the process switches between two regimes. It can be written:\n",
    "\n",
    "$$\n",
    "y_t = \\mu_{S_t} + \\phi_1 (y_{t-1} - \\mu_{S_{t-1}}) + \\phi_2 (y_{t-2} - \\mu_{S_{t-2}}) + \\phi_3 (y_{t-3} - \\mu_{S_{t-3}}) + \\phi_4 (y_{t-4} - \\mu_{S_{t-4}}) + \\varepsilon_t\n",
    "$$\n",
    "\n",
    "Each period, the regime transitions according to the following matrix of transition probabilities:\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00} & p_{10} \\\\\n",
    "p_{01} & p_{11}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "where $p_{ij}$ is the probability of transitioning *from* regime $i$, *to* regime $j$.\n",
    "\n",
    "The model class is `MarkovAutoregression` in the time-series part of `statsmodels`. In order to create the model, we must specify the number of regimes with `k_regimes=2`, and the order of the autoregression with `order=4`. The default model also includes switching autoregressive coefficients, so here we also need to specify `switching_ar=False` to avoid that.\n",
    "\n",
    "After creation, the model is `fit` via maximum likelihood estimation. Under the hood, good starting parameters are found using a number of steps of the expectation maximization (EM) algorithm, and a quasi-Newton (BFGS) algorithm is applied to quickly find the maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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JP//5ANwlLmIuzPpxZnoR776sA3YTG8W7vrZ36xlvKA6zTgW1OGbXZlAjlkxl7BBwqsvpaR8uzgWK+q4Mu4Iw61TSzilTgKe9XAEGgN8A8BVK6ZsBzAJ4S/UOqTY4zMJJ1+mvvtrzvnsP4pM/PlH1560WB4fdAIDBufWldhbDQiiGZIpmFcCAsLpdTx7gk6L6e6DHhmFXsG6jvljHfaUK8Jy4mD08ulDU/V2BKIacQVy1qRGAsL1394FO/PDQGMbd66/Dud5IpShC8STarGIBXIECzLZyP/eOfiyG4/j0AwMlqYcPHJ+ESkFw5752NIo+VDe3QawYC6GYNAEOAJ8GV2MopRh1Cee4ExPegvcfcgawudkEQoTGcYdZCwXBuktLKasAppT+F6X0KfF/mwHMV++QaoPDIirAVS6A48kUzs348fiZWRwdK+5CvNIcHBIK4CFnoKKmkbUIW/DIF8AmjHtCSCTXhy/81KQPhAB3X9mFZIrW5YInmkjCJRYalSrA7Lt8fnaxqMEKTCm+atPSQJxP3rYNCkLwlacuVHQsnMJEEklQCrQ1CGpSJcMwPGKhdO2WRnzq9m148uwcfna0uCbnZIrioeNTuHl7MxpNWtiNwrmBN8KVD6UUL150Fr3o9gRjUgIEsGSF4FFotcEZiEoNv8UUwMPOILaI9gcAUCkVaLWsvySIijzAhJBrAdgopa8tu/3jhJAjhJAjTqezogOsFo1GDQipfgE84VnqRP7yE+frzsOUSlEcHHbDoFEimkhVXHSsNfIWwE1GxJMUExUqkfXCyQkvtjSbcKU48bAebRBzPuH9IKRyBdjpj0CpIKAURcWqHRrxQK9WYk9Hg3Rba4MOH7l+Ex4+OV2Xf6/1BBuDvGSBqFwBths1+OgbNuPqTXZ87hdnimqsPDjkxtxiFO++vFN8DqH4cge5F7xcDg65cc93D+NXp4rrM/GG4rClTd5j/80V4NowIlr9FKRwARyMJjDji0gNcIw2qx4z3AIhQAixA/gagN9a/jNK6b2U0gOU0gPNzc2VHF/VUCkVaDRq4PRX9w0cdQsfrLv2t+O1YQ9eEmN16oXzs354Q3G867IOAIIfeCMhFcAmeQUYWB9RaJRSnJz0Yl+nFT12AwwaJc7WYUE3LW6hbW8xY8obrmjBOO+P4ooeG9RKgsMjhXdfDo94cHmPFRpV5mnvo2/YBEqBlwbrY7G+XgmJEWitrACuIAvYE4pBo1LAoFFCqSD417v3gRCCT/3sZMHHPnBsEmadCrfucAAAV4CrwHdfGQFQfJN5tgVCLd2+FplfjNT1+YPVKddvbcKJCS9SeXaCR1zCfTc3GTNub7fqpfP3eqHcJjgNgJ8B+DSldM1Ml2g266ruAWZNVJ+5Yyc6rHp8+YkLdaUCM//vPdf2AgAGN1oBHMitAG8pEIX26MDMmknOmPKG4QrEsL+rAQoFwfZWM87P1l8BzDxkB3ptCMWSUjNTOcwvRtFjN2BPR4MUb5YLXziOc7OLuKq3MetnTSYNtCoF5he5AlhLmALcaNRArSQVK8BsjC4gpLp84qbNODTiydvkE4wm8PiZWbx9bzt0YhqFVa+GgvACuFzG3EE8c15wQRZbwC4EY5LtAViKQ1urjYhfeeoiPvq9I3V17U9n2BWEWknwtj1t8EcSGHHnbv4eEgWhLY5MBbi9QYcZXyRv8bzWKFcB/iiAywH8FSHkeULI+6p4TDXDYdZW3QIx4gqiQa9Gi0WHP37TNgxM+fD46fpJWzg45EZPowHbW81osWjr0hdaS5z+KAwaJYza7KnfVoMGdqMGwzJRaJRSfOFX5/DNF4ZW4jAr5pSY/7u30woA2NFqwbkZf92dkFkXMbNplGvJSaUonIEoHBYtrtxkx6lJb17/4dExDyjN9P8yCCFoseiqfm7gZMIUYKNWhQa9ujIPcDCeUUABwGXdNgDAuTwRgE+fm0MolsS7L++QblMoCGwGzbqbBvfqkAtv/rcXaj7s5XuvjkJJCExaVVE5s7FECsFYEvY0BdiqX9sK8KtDbsSSqYqSTWrJiDOIbrsBl/cI35ET47ltEEPOIBQE6Gk0ZNze1qBDLJFaV9+TcpvgvkEptVFKbxb/+b9qH1gtcJi1VVd5Rt1BbBK3Ct51WQe2Okz4lycv1EVjVTJFcWjEjeu2CKpXn8OMS/P1mw9bC5z+7Clw6WxuMmJIRgEec4cw5Q3DW8FFeiU5OeGFRqnAjjYzAGBXmxm+cLzugstnfGFYDWr0OYTjLNcH7A4K6R4Osw5X9doRT9K83rZDIx6olQSXdVtlfy4sjuvrb7XeCIoRVwaNChadurIUiFBMmiLG2NVmAQCcmfblfNzhEQ/MOhWuEItlht2oWXfDML7/6iguzgWkoQa1wB+J42dHJvG2vW3otOmL2tGRhmCkvX8qpQIWnWpNKsATnhDGRe+5t04LeKFOMWFLswkmrSrvuXLIGUCX3QCtSplx+9IwjPVjg9gwgzAAYRvcFYhWVcIfcQYlr4xSQfCpN2/DkDOIB49PVe01yuXMtA/+SALXbBYK4K0OEwbnA3WnCtYSuSlw6QhRaNkF8KticsZaOSGfmPBiZ7tFOmntFIuBemvsmvFG0GrRocMmnEzLVYBZseowa3Ggxw5C8ucBHx7xYF+nVdr2Xk6LRcctEDUmKCqRJq0KZr26whzgWEYTFSA0UrU36PJ6309N+rC3U7AJpWM3ataVBcIXjuO584IntZbDC35+dBKBaAIfuX4TbAZNUQUgS/CwLVPwbWt0GhyzGQL1aaNJpihG3SFsbjZCqSDY29mQtwAeTqtp0lnKAuYF8JrEYdYikaJV+5JF4klM+yLoTfuw3N7fir2dDfj3pwdXfTgGiz+7ViyA+1pMCMWEY94oOAMFFOBmE1yBaJYf8dUhoZlxMRKv++i4ZIri9JQP+zuX0g12rFIBPOUN57UATfsiaLfq0aBXw6xTla0AM7uCw6JFg0GN7S1mHM7hAw7FEhiY9MnaHxjNNbBHcTJhBbBBo4RFp6o4Bzh9C52xq92CM9Pyn/loIonzs4vY05G9C9Bo0qyrFIjHT88gJu5C1iq6KpWi+P6ro7is24r9XVbYjOqiFGAWdbb8/bMaNBX1BKwW7DoL1KdgMu0NI5ZIobdRqFP2d1lxbmZR1jKWSlGMuAJZCRDA+hyGsbEKYIvQfVytCx3rrNyUVgATQvD7t2zFlDeMI0UG9NeKg8NubGk2Sr8323YenNs4NohiLBBAZiMcpRQHh9xQEIDS0gL7E8kUvvT4+RXdJhpyBhCMJSX/LyCobN12Q14/ZC349AMD+L0fHkU4x0SnWV9YisHqtBkwVWYB7BTVWjbg5qpNdhwbW5C1Hh0f9yKRonkLYIdFi0A0IRVp9ciF2frzdJcCm/LFPMDlFsDJFIU3HM9SgAFgV3sDhp0B2c/fhVk/4kmKvWkLRYbduLaKr2SK5vVQP3xiGr2NBhg1ypoVwM9dmMeoO4Tfun4TADbOuLC4JFkglhXANoO6KA9xPUEpxatDLilasR4VbJbqwOqU/V1WJFJU1io07QsjEk9JCUnp2AxqaFUKboFYqzjM1R2GwbL1Ni3bLrhavNAWEzhdK+LJFF4f8eDaLUtd731iV+dGiUKLJpLwheMFLBDZUWgX5wJwB2OSdaQUH/DAlA//9fwQnjwzV+ZRlw77nO3rylS2draZcW4FkyBOT/nw4kUnUnSpkzidsJj6wJSETpu+AgVYUCHY4ubKXjuCsaTs9vehEQ8UBLiix5b1M0aLubqL42pzeMSD2//9RTx/sX6jlgoRjKUpwHp12SkQvnAclAL2ZVvogOADTlHggswi/6TUKCpXAGulqZFrgR8cHMW1//SMbO7x3GIEB4fduGt/Bzps+rIXmYW475VRtFp0eMvuVgBiARuKF1yksYWGzbjMAmFYexaIYVcQc4tR3LGnDQDqchHFhLrNYurRfrEP4rhMIxwTgtKHYDAIIeiw6rkCvFZhF8v5xeq8gSxKpHdZAWw1aLCpyYiTq1gAD0z5EIwlce3mJuk2m1GDJpNmwyRBsNGm+RTgbrsBSgXJUICZ/eGt0kmt+JPy6SnhIruSnbKnJr0wa1VZvq0drRaMuoI51dhq843nh6ASvZWDMs2WTDlYUoD1mFwIlaVqzvujaNCrJU8vU3cPy/iAD4+4sbujAWZddsHEkCZFVuncUG1+dWoaAFb1nFIpoWgSSgWBVqUQm+ASZb33zGcppwD3t+duhBuY9MJu1KBDXIClYzeoQWn9NjEt59nz8wjFkvjSE9kTDB85OQ1KgXfsb69ZduvFOT9evuTCh67tgVoplBE2gwbJFC3o7V6QPMDLLRDqurQQ5IP1itze3wIFqc/Pz7AzCINGKQmADrMOHVa9tCBMhwkXcgowALRZdesqC3hDFcBsu7TYsO5CjDiDcJi1MMlEbO3vsuLk5OpdrJgv6ZrNmdu+QiPcxrBA5JsCx9CoFOi2GzKi0F4dcqPbbsBu8WLqK+GkPCAWwJ4V9BOenPBhb1d2Y8/OPGpYtRlxBfHo6Rl85PpeqJUEF2UWWSyRgo3C7bQZEIwly7rozS9GpRM6IDSxddsNWXnA0UQSx8e9uKo3t/2BPR4A5upQAaaU4smzwo5CvTU1lkIwloBBowQhBBa9CrFkCtFE6Wk5uQooQFhUmXUqnJXxAZ+a9GFPR4OUHZyO3bR2hmHEEikcGV2AWafCIyencXQs02r38Ilp7OlowJZmE9qttVGAv/H8ELQqBT5wVbd0m03K8s3/N1wIxqBXK7MaUm0GDQLRBGJlfCZWi4NDLrQ36LCpySh6mOvv8zPiCqK30Zjxud/X1YATE5mfG0opHjs9iyaTFk2m7O8WIJy7eRPcGkWvUcKsVVWt23vUHcxSfxn7OhswtxhdNb/MwSE3drSa0bhs+38jJUEUUwADgg+YKcDJFMVrw0J0nBTOHi5FARYuvO4VilSKxJM4N7OY4f9l7FrBRrj/fmEIGqUCH79xCzY1GWV3GdiJs90qFJtMiSvHBjHnj0iqLePKXjuOjC5In+1ANIHf/d9jiCZSuHFb/omUjirvDlWTU5M+zPgidTvdr1hC0SSMGkEsaBBzX8vJAvakjUFeDiEEu9qyG+HCsSQuzvmxT8b+AAjDOYCV3bkpl4EpL8LxJP7uzn40m7X4h1+dlT7zQ84ABqZ8uGt/OwDhO7YQiksZzNXgsYEZPHh8Cr99w+Zl44xZlm/+93QhFM9KgACWUiFKOd+uJqmU0CtyzZZGEEJgNailBr96YtQdxKZllob9XVZMeMIZQ2N+fnQSh0c8+NSbt8kuEgGhEW7eH0W8DmJeq8GGKoABoNmirdo0uBGXfFwIsOTHXI0ty2giiSNjHsnDmk6fwwx/JFG3Xsdqkm8KXDqbm40YcQWREhsD/JEErt3SuBTOXuRJLRIXLrLAyhXAZ2cWkUhR7JMpgDttepi0qpoXwLO+CO4/Nom7D3Sh2axFn8OcwwIhFJdMbe2sIApNUIB1GbddtckGdzCGIWcQkwshvPcbr+KFi078wzt3FyyAG/RqaFSKqk+KrAZPnJmFUkHwgau6MeEJw1/BBLXVJBBLwKAVVD+LaEcppxGOKYxyFggA6G9vwPnZxQw/79kZH1IU2CPzPQGWium1oAC/Nizscty6w4E/e/N2HB/34penhImVvzgxDUKAO/ctFcBA9aKrZnxh/OUDA9jb2YBPvrEv42dMMCikgspF2KU/fq3YIC7M+bEQiuO6LYLN0F6HCnAskcKEJ5RVp+zvEgdiiPWJJxjDPz56Dgd6bLj7QFfO52tv0IFS4Zy/Hth4BbCpOgXwYiQOVyCWUwHe2WaBWklwYiJ3KHutODnhQySeymiAY7BGuI3gA2bvc6OxUAFsQjSRwpQ3LHm6rt3SCIteDUKKb4K7MOtHIkWhUytWLFLplHgC29+VfWFXKAh2tJpxvsZJEN95eRgpCnz8xs0AhLi9cU8oK2ZnxhdGo1EjbX122YRJQ6V2qVNK4fRnWiCApely33l5BO/8z1cw5Q3j+x+5Ch+8pqfgcxJC4DBrMVeHCvCTZ+dw9SY7rtsqfJ/Pz65NC1MompDsYhZxcVlOI5wnR4wWY1e7BZF4SuqsBEmvAAAgAElEQVR+B4RzIiDfAAesLQWY7e7ZjRq854pO7Gyz4IuPnUcknsTDJ6Zw7eZGaZHJ8ranqtC4lEpR/OlPTyKWSOGr779M8v4ymAWiUJLDQigma19hi5C1kgSRfq0A6jPGbdwTQopCikBj7OlogFJBpAL4nx49B38kgS+8a0+WlS6dpWEY9XeeLIcNVwA7LLqqTHwadcknQDB0aiV2tVlWRQF+7PQMCAGu2ZRdAG9tEQvgDeADdvqjsBkEZS8fUhSaK4hXh9zoc5jgMOugVBBYdGr4ilzVnxYbb67d3LhiF9KTkz44zFq0Nuhkf75DTIKoleXFG4rhh4fGcefeNnTZhYK2z2EGpdlpIzO+CNqsS8dp0atg1paeBewLxxFLprKU/U1NRjSZtPjx4XEYtSo8+HvX4w19TTmeJZtajEqX49K8v2hr1JAzgEvzAdze31q3w02KJRhLwqBhCrBQCC+GS9+aXwjFoFMroNfIDzWRa4QbmPKhxaKVCsPlMEWy3qfBxRKpjN09pYLgr9+2E1PeMP70Zycx6g7hnfuXxjyzgqUaPuBvvTSMV4fc+Ow7dsle9+ySApy/CPSGssdYA5Buq7ciMhcHh1zobTRIKrvNoK67JjipTllmgdBrlNjeYsaJCS8ODbvxs6OT+NgNm7G91Zz3+Zh9bb34gDdeAVylixxTF3JZIADBBnFq0rui0Tqnp3z4wcEx3H1FFxpkTjLNJi0a9GoMboAotEIZwAzW8XphdhGvj3ik0dGAcFIu9oR8esqHBr0a+7qs8IbiNfdJzfoieGnQKav+Mna2WeCPJMqOGyvE918dQyiWxCdu3iLdtq1FPm5vxhuRGuAAMVZHTIIohaUhGJnFDCEEH7iqC2/a1YKHfu96bHXIdzLnwmHWrUgB/FvfO4K/eehMUfd94owwVORNu1rQatHBalDLNnjlYtYXyWqSWi1CsUSWB7g8BVh+CAZjS7MJGqUiwy99ctIrOwCDoRZH8a5k82o5nJz0IhJPZdjbrt/ahNt2OPCrUzPQKBW4XYwlA4AWsxZKBam4YDk95cO/PHkBb+lvzblFbtapikpC8ASzx1gDaQpynRWRciSSKRwa9uDaLZkpS/V27PnqlP3dVpyY8OKvHjqNTpsen7ytL+s+y2Hn7/WSBLEhC+BQLIlAhYH3I64gCIGkesmxr9OKYCwpm4laCxLJFD79wABsBg0+c8dO2fsQQtDnMOHSRrBAFJgCx2gyaWDWqvDAsSmE48mMk5rVoCnaAjEw5cPuDovUeFjLrTxvKIYPfecQIvEU/jDPiauaqiGlFJMLITx1dg5fe2YQv//DY7j3xSHctsOBHa0W6X49jUaoFETyQzOmfWG0L1Oqy8kCZk2sLTLv7Z+8eTu+dc+BnP7QfLRYam+BcAeiGPeEcKrIhJgnzsxhb2cD2q16EEKws9VS0nv5H88O4sP3Ha6LptdQNAnDMgtEOU1wC0F5DylDo1Kgr8UkLRT8kTiGncGcDXCMRpO27i0Qrw25hd29Zek+n75jJ5QKglt2NEuLCwBQKRVotegqGoYRiSfxhz85jkajFl98z56cDVIKBSmYhCDEpMWzhmAAa6sAPj29CH80kSWWROKpFYudLIZhVxA2g1r2772/ywp/JIFL8wH8/V27c+6opMOG2HAFeI3CCqJKfcAjriA6rPqsKJd0WOD0Sg3EuO+VUQxM+fDZd+ySVX8ZfS0mXJzPnir18qAL4+7SG5LqFac/iqY8QzAYhBBsbjbi/KwfhCyNjgYAq764ba1YIoULs37s7mhAU439hMFoAh++73WMuUO4954rsLsj94V9R6sZhKAqE+G++swg3vDPz+G3f3AE//rURZye9uHGbc342zt3ZdxPo1IISRBpCnAgmoA/kkDbsgzWTpsBkwvhkgo0VqQuV4ArxWHRwR9J1PQCxmLy5v3RglasWV8EJye8uL1/SdHb1W7B+Vm/7MQ7OSY8Ifgjiboo7IKxBIziRdYsWSDKUIBzeEjT6W+34Oy0YP1hf/M9BQpgex0qeMt5bcSNHa2WrIJmq8OEH33sanz2Hf1Zj+mw6isqgP/v9QkMO4P40nv3yhZS6RRKQmBDTORSIPQaJbQqxZpogmNZ8elKfD0W8KOu3ElVl4k7h3fsacUtOxxFP2dbgw4z62QYxoYrgFnneKVxRyOuYE7/L2NToxFmnWpFCuAJTwhfeeoi3rjTgbeJAxxysdVhhjcUz7goHhxy40PfPYRP/fxkrQ91RWCNUvmmwKXDbBC72xsyFg+2IsPZL84JY1b3dDRICnAtkiBiiRQ+8b9HcWrSi//49cukDuRcGDQq9DYacXS88m3wU5M+dNsNuP93r8OZz92OF/7sFnzjg1egpzH7e9DXYsoYuT3jzRyCwei06RGIJkrygkoWiCLU/VJYmhRZu5P7QFr4/PKoruU8eVawP9ze3yLdtrPNgmgiJU13KgRrVhmXmRi20oSiSRhEC4RWpYROrSg4NEGOQgowIEQAuoMxzC1Gpb+5XFRgOjaDZsXSW8ohmkjiyOhClvrLuHpzY4bFiNFu1ZXtAU6mKL798jAu77YWTFIBCk9zyxdhJz2+DhZrhTg45Mb2FnPGDqNN8jDXz/Hnq1P6Wsz4j1+/DP/0rr0lPWelC6p6YuMVwJbKxyFTSosqgBUKgn2d1po3wlFK8ZkHB6AgwOfv2p1zi4qxPAnCG4rhj//vBAiESVrrQQUOxpIIx5NFWSCAJY/UdcuSM4qdb89Upt3tDdLJvdpJEMkUxZ/89AReGnThi+/eK40gLcRd+9vx4kUnXqhwjO6ML4I+hwlX9NhglBn+kk6fw5yRBDEtFmLtWQqw8P8TJfiA5/0RGDXKgsdQKkxRrqUPeGDKh1bxdc5M5U+IeeLMLDY3G7HVsdSYsrNN+O+zRSr6LK5IbmTuSkIpFRRg7dKOWYNeXZ4CHIzJjkFOp1/cFTk748OpKR86bfqcRRej0aip6xi0kxM+RBOpjB2qYuiw6TG7GCmrF+WJM7OY8ISlhJdC2AokIbBzaS4lOVfPRT1YeBixRAqvj3qyUpZsdRbjFowmMLsYydun9I597Xl3i+Vos+p4CsRaZUnlKf8i5w7G4I8kChbAgOCzOT/rz4qEqiYPHp/CS4Mu/PlbdmQVGHL0SU1Kgg3iL+8fgDsYxTc/eAUIAe4/NlmzY10pih2CwWB/k+u2ZiqqDXo1FiOJglvOp6d8MOtU6Gk0SFN0qq0mffGxc/jlqRn85Vt34O4rc2c1LucTN23B5mYj/vqhgYq292d84YwUh3z0tZiQokujNZkC3LrMttBhFTz0pfiA5/3RqtsfgPRhGLUtgK/ZbEdPoyGvAuwNxfDasCfD/gAIW90qBSnKB7wYiUu9DiuxqI0nU3j67JxssRKJp5CiyFi0WHTqkj3AiWQKi5FEQQV4h9jNfnZ6EacmvTnjz9KxmwT1sp6KrXQOiv7fq2XSffLRbtUjmaIl+9sppfjvF4fR22jAm3YVt9gulITAils5C4Rwe7bg8PCJKVz5hacr7tupFsLCPpX1mWKfyXpRgNkuUS4LRLl02QzwheN1vVgslg1XADfo1dAoKwu8Z9EixXyw9nVZkRQHLNSCWCKFf/jVOVzWbS0q7xQQihCTVoXB+QB+8voEHj8ziz+7fTve3N+K67c04f5jk0itYHJFLSi1AH7jzhZ884OX48ZlsVnsRF1oq/b0lA+724UxqxadGioFqaoC/NPXJ/Ctl0Zwz7U9+MRNWwo/IA2dWol/fNceTHjC+PdnLpb1+mFxZLHcFqsc21qEAoQlQcz4IiAEWXFt5QzDcC4W19xYKtI45Bo1ws37I5jxRbC7owG72xuk2Dw5njk3j2SKZhXAWpUSWx2mogrgdJ/e2AoowI+fnsXHfnBEdvR2UJxEZkxrtLHo1SWnQLCG1EJqrlmnRk+jAS9fcmHCE86bAMFoNGoQT9KybBkrwWvDbuxqs5Ss2JU7DOP10QWcnPDiozdshjJPNmw6hZIQmL0hl4fbZlRnPD6Vovjas5fgCsQwVCfJRbmu//UW4zbqEr7zxQh1pcBSh47VSbpMJWy4ApgQgmaztiKf33AREWiMfV3CKvH4eG1sENPeMDzBGD5wVXfRJylCCLY6THh50IXPPXIGb9jahI+9Qdjieu8VnZhcCOPQiKcmx7tSlFoAq5QKvGV3W5Z9pJjpRvFkCudm/djdISQhKBQENmP1/ISHht34q4cGcENfE/727bsKP0CGazY34n0HuvDtl0bKWoyx3NrlHt5c9C5LgpjxhdFs0maF51sNahg1yhIV4EjV/b+AsNhRK0nNLBCnp5a8qP0dFkx4wvDluFg+eXYWrRYd9so0OO5qsxQVhcaiinRqxYp4gFlhIKegh6LCzgPzAANCFnCpOcCFCqh0+tst0tS0QgkQQH1Pg4vEkzg6viA73bMQrAAu1bd574vDsBs1eO/lnUU/plASwkKBKX6CArz0nXhh0CktoldiEVcMTFndtKz3waqvr0EeIy7h77Z8CEal7OuyQqUgOMIL4LVJs7myaXAjriBUCiKdWPLhMOvQYdXj5GRtFOBZUa0qVplj9DlMGHYFYdCo8JW790nTX27vb4VJq6qqDSKZorjvlZGcF/ta4BQXOMU2weWCqS35fF2DcwHEEqmMNIZGo6YqnfcTnhB+94fH0GUz4Ou/fjlUyvK/sp++YwdsBjU+88BAyX5A5vkq9nOmUSnQ22SUfObCEIzsxxJCpCSIYqCUYk5mDHI1IISg2VTZ4jgfA5OLIEQozPrbhc/KmZns80IskcLLgy7cutMhO5VpZ5sF8/4o3IH85zCmAF/ebVsRDzDzccstFiUFeLkHuEQFuFATVTq72pai+frzJKUwlgrg+ssCPjHhRSyRKqsAbi+jAL40H8DT5+bwoWt6iorHYhRKQlgIxaFWkoydgOWPXwjFpB3I7748IiX5jBfZ+FlrxtwhWHSqrGEeGpUCJq2qbiwQw64gWi26qvdK6NRK9Hc0bGwFmBDSQgh5qZoHs1I4zNqKfH6jriC6Gw1FFyP7uhpq1gjHtmtbG0or9Fg+7JfeszfDT6nXKPG2PW14dGAGwSp5ro6NL+Bzj5zF3//qbFWerxicgSiUClKUUpQP9nhfOPdJjSl7e9Iusk0mbcECpRD+SBwf/f7rSCRT+PZvHih563M5VoMGf3tnP05O+vCDg6MlPXapAC6+8OxzmKQotGlvdgYwo9NWfFdxIJpAOJ5Ei6X6CjAgToqskQd4YMqLLc0mGLWqpWllU9lK7pFRD4KxJG7O0XW/lO2cvxFuxheGggAHemyYXYzUtA8BWEqakNv5CIkFcIYCrC/dA7wgNVEV/i6wRcbmJmNGNm4u2Mj0ekyCeG1Y8P9etUk+ASIfRq1QrJVigfjOy8PQqhS459ribHWMggVwUIiwy9WobTWokaKAP5LA+dlFvDTowkeu70WzWYuxOmnOHnUL0WJyv4O1yNSglUCIQMs9p6ASDvTYcHJSWJStZcoqgAkhNgDfB1BdbX2FaDZr4aygOBlxBbO2P/Kxr9OKcU+o4oJIDtblnWvEZy4+cHU3HvmDN+CNu1qyfvbeA50IxZJ47PRsVY6RqYA/Pzq5YlOphAxgTd655sVgFS+c+bItB6Z8MGlVGVtN9ioowH/+81MYcgbxX79xhRTTVil37m3DTdua8eUnLuDoWPE2F6mJrZQCuMWMMXcQkXhSUIBzqMelTINbmgJXowI4jz1q2BmoqIg8NemTLA1NJi3aGnSyPuAXLjqhVpKshkzGUhJE/l2laW8EDrMOm5qNoLS0RsNymPAIzy+rAIsWiHQF2KITUiBKaTrzBIvzAANCZjJQOP+XYTfVrwXi4JAb/e2Wogp5Odob9EVHoTn9Udx/bArvvaJTinQsFluBHbOFAhnO6QX0d18egV6txG9c3Y0eu6FuLBBj7pBs9CNQX1nSQlJVda4byznQY0M0kapZb9NKUa4CnATwPgBrcii9w6yDJxgra/WSSlGMugtHoKXDTOOnamCDmF0UIqHMutJOjDq1MueF4UCPDT2NBtx/tDo2iEvzAejVSrRadPjbh0+vyGjoYscgF0KKtsmjVA1M+bCr3ZJRbDeaNPBUoCSlUhRPnJnFh67pwRv68mf9lgIhBF94127YDBq895sH8dlfnClK6Z9ZjMBu1OQd/LKcPoeQBHFiwotQLCnNkV9Op00PfySRoQY+e34Ov/M/R+BftkXO1NlaWCAAYSE5J6MAB6MJvPWrL+E/nhks63nnFiOY90czvnP97RbZJIjnLzhxZa8dphxbl40mLVos2qIU4DarDt3itMpa2iDiyZTkE5crIOUVYBVSVIgsLBbJQ1rEzo7DrMVvXN2dc3Tvcth45XoYGpJOMkVxfMJbcvpDOh02PaaLHF7wPwdHEU+m8NE3bCr5dQolIXhD8bzqvc0o/OzSfAAPHZ/Ge67ogNWgQXejoSZJJk+cmcXPS7jOxRIpTC6E0Nsor6xaC8TArRTeUAwLoXhRfUrlcEWPDQDqZsx6uZRVAFNKFymlOas5QsjHCSFHCCFHnM7KskdrAVOPXMsU2cdPz+LX730tbwKCsJWYwqbm4j9YuzsaoCC1mQg3txhBSwmqXDEQQvCeyztxcNhdlYvm4LwfWx0m/NXbduLM9CJ+dGisCkeZH2eg+CEY+TDrVCAE8OU4oSeSKZybWcTu9szFRJNJC380UbZiuBCKIUWBnhwn2krotBnwxB/fiHuu6cH3Xh3F7f/+Il4edOV9zIw3XJL9AVhKgmD5w7nU404bi0ITPms/OjSOj33/CJ44M4dnz89n3Jeps7VogmPP6wvHs963kxNeRBMp/GpgpqyYLDaMId0m09/egCFnQCoOAcEqcmHOj5u35x86sLOt8EjkGV8E7Q16dNuFc1UtG+GmvWGw06ZcARxgCnBaAczUzFKygD3BGAwaZVELMWGxtwfX51DSl6PXKKFXK+umiYkRiCYQS6RK/v6lw4YXFPrsUkpx/7Ep3LytuaxdJykJIcff0BOK5VXvWdPx1567hFgyhd+6XijCe+zGmth4/vuFIXzrxeGi7z8lfs5zKcA2g7ouPj/Mera5hDqlFBwWHbrsehwZ3YAFcCEopfdSSg9QSg80NxeeHrPS5MoCvu+VERwcdkuNZXKMuOQ7QPNh1KrQ5zBLwxKqyawvkpWtWg3efXkHAOCBY1MVP9el+QD6HCa8fW8brtvSiC8/caEmdpB0qqUAKxQEDXr5cHYAuOQMIJpIYU+nJeP2xgo7yl2ielzMKOdyMGlV+Nxdu/GzT1wLjVKBD37nEL76dG51U7AwlPY5620yQKkgeFEsgHNZIKRhGJ4w/vXJC/jMgwO4cVszGo2arALY6a+tAswWx8ubZI+Jk/TG3CHZmK9CnJryQUGWtuUBYWFMKTIKWbZYuHl7/tGku9osuDQfQDQhXxBQSjEtLlqaTBro1cqaeiiZ/UGlIHkV4OUWCAAlNcIV2kKvFHsdDsNg+bdsfHQ5dFjFiYsFIt4G5wOY8oaLzv1dzpKFQf499YZieccps8efnPDith0OqQhnQkC1dzHG3KGS8oWlbN0cwkShSXgrBVtw7y6i+bNcrui24ej4Qt3mZhfDhk2BADIvcvP+CA6PCp7IfGNGpQK4xJXVpiZjTRSYucVoTQrgTpsB121pxP3HJiv6gPsjccz4ItjaYgIhBJ97Rz9CsSS+9PiFKh5tJqkUhSsQq1pWrM2gyWmBkFP2gMojldjuRK0KYMaVvXY8+skbcENfE350OLcyn8/DmwutSonetIEPuS0QwsXk84+cwdeevYT3X9mFb99zADdtb8YLF50Zlpl5fxQalQIWfXU7mxlL0+AyF8HHxr1osWhBiLBTVCoDk170OcwZFgAWm5dug3j+wjzaG3TStMZc7GyzIJGikr9+OQuhOKKJFNqsehBC0G031FQBZgkQO9ssBTzAmU1wAEpKh1kI5lcQK6XRVJx3f34xgo9+7/UVUfuYDahUm1s6UhJEAR/wc+KC85Yd5QlXaqUC5hxJCJRSLITiOYdgAJkDMj56w5IFo1ssOEtZxH3yJ8fxtw+fzvnzxUgc7mBMSigphjHx+p9LAbYa1PAXMTip1pye8sFh1pbcG1QKV/Ta4fRHpcXvWmRDFsBMPUq/yD1xZg6szsv3JRtxBaFTK9BSogLVYROaEKq5WkqJ032qbYFgvHN/B8Y95SleDJbh2CeOc+1rMeMj1/fi/45M4Ph4bbZPFkIxJFO0KhYIQNiqzTXd6Mz0IgwaZVazAWseWW6zKZalArh2F3uGTq3EtVsaMbcYzfLcAoJ65wvHi54Clw5735UKklO1tRnU0KuVmPZF8Cdv2oZ/evceqJQK3LrDAW8onvE5mVsUMoALjfsuF7lpcJRSHB9fwI19zTjQY8MTZ+ZKek5KKQamFrPUmFaLDnajRkoRiSVSeOWSGzdtdxT8/ZaSIORtEMyPy5I3uuyGmnqAJzwhqBQE/e2WnAqwggBa1dIlZ0kBLr4A8YTiBafAVUKxCvDzF5145vz8inggA+LfJ5cnvBg6bMUNw3j2/Dx2tllKXuymYzXKJyG4g8J5Od+i3qJTQ0GEz3f6yOce0cdebCMcpRTPX3Di5Uu5rV1j4qAIllFdDKPuEExaVc7zcjE9IyvBqSlfUdMPK+EA8wGPr92ZARUVwJTSm6t0HCtKo0kDQjIvco+emsHmJiPUSpK3AB51BdHbaCw5XaDdqkc4nqyqQd4VjCKRohV5w/LRLypUlyqYwDMoFcBLBeIn37gNDrMW//joucoOMAcs4aO5Stvk+aJtLs0HsNVhyhpCUuk45FpbIJazWSzg2Q5HOuVEoDG2iSOmW8zanINaCCH45Bv78NX378cf3tYnFX839DVDqSAZNoj5xWhNVY0WSQFeOjeMukNYCMVxeY8Nt/e34tzMYkkNObOLEbgC0awLEiFCwXhajEI7OraAQDRR0P8LCDtKOrUiZyMcywBm2cs9jYICXKvtynFPCO1WPZpMWiyE4ll9FMFoEkaNKqOwZyp+KR5gIUarsjjAfBRbAA+KogAbNlJL/FWwQLDdl3xxg75wHEfGFnBrmeovI5cNYLSI3VOFguBP3rQNn7+rP+OzYjdqYNKqis4CnvdH4QvHMe4OIZ5DjWU7vbFkquiG+FF3ED2NhrwxbgDyjoOuNYFoAkPOQFHTDythW4sZZq1qTfuAN6QCrFYqYDdopELJFYji0Igbb9vbhi6bAWMFLBDlGMvLHUeZjzmfcPy1Kgg2N5lACDA0X34A+aX5ADQqBbrsS54pk1aFXzvQiWPj3ppkk5Y6Ba4QggVC/oQ2sRDK+N0YbJu23HHIrkAUKtF/vBJsdQif6SFn9mJHKqbKUIW2io1wckMw0vnETVtw1/6OjNsa9Goc6LFlFsA1mgLHsBs0UClIxjhkFvh+WbdVGk38xJnibRAs/UUudWV3RwMG5/2IJpJ4/uI81EpSVNOWUkGwvdWSMwptuQLcbTcgHE9WFP+Yj4mFMLrsetiMGiRTNMvXG4olYNBmNq5JTXCleICDtfUACwNsCv+NLojWk1Knq5WDP1J5Adxk1EKjUuS9/rw0KNiNbingPy+E1aCRtYYUO0H1D27tw5W9mXnHhBD0NBYfhcYmUCZSNKeglX6dLzbzfswdyjtZzW7M74FeCc5M+UApsvpSqo1SQbC/27qmkyA2ZAEMCMURU4CfODOLFAXu2NOGnkYDRnN8YRLJFMY9+b8AuWCNPtXM4mTNerXwAANCV3SHVY9LMkVRsQzO+bG5yZil/u1ub0AyRXFhtnx7RS6qXQA36NXwyuQAJ1NCo1GXLbsANmlV0KgUZUcqufxRNFYhx7hYuu3CezTslFOASxuDnA5T/svdpbh1hwPnZ/3ShXveH61pAaxQEDSZtBkK8LHxBZjERtYuuwH97RY8XkIBfHrKB6WCZEwmY/S3WxBPCl7eFy44caAnd/zZcthIZDlVd9oXgVpJpB2EWkehTXpC6LYbcjZ/BmPJjAQIYGlLv9hhGLFECv5ooqYeYLtRi0g8lZHMIcdF8bw1U2S0WCUEpAK4/MWwQkHQ3qDDZJ4C+LnzTlgNalzWbSv7dQDAbpBvGh5xBaFWFjdBVY6eEqLQ0q8rwzmuXyOupecqphEukUxhwhPKm8zDFmer2UjJmu1r2QDHuKLHhgtz/pInOtYLG7YAdlh00rjcxwZmsanJiB2tZvQ0GjHuDspeVCYXwkikaEkZwIxy57HnQyqAa2SBAIAtzSYMVWCBuOQMoE9UAdORRsHK5KBWiitQfQXYH01kbaXNLkYQT1J02eVH/DYZNRVYIKIrZn8AhDGe3XaDvAJc5rAVQIjhYc9dDrftFNSo5y7MIxJPwh9JZEwurAUtFm2mAjzuxf4uq7SIu72/FUfHFjCfJy0mnVOTPvQ5TLLRXSw+7+lzczg/68dNRdgfGP3tFixGErKL6hlvGC0WnbSAYrsUtWiEC0YTcAdj6LQZcubABqPZCrBKKYyOXQwXp76xbeVaeoBZAZ/ve+sLx6VzbzV39HLBfPmVeIABlgUsf7ypFMULF+dx07bmnFalYrHmsECMOIPothc/QXU53XYjJhZCReXID84FpL/XkMyiHshUgENFZFFPeyNIpGheAaweLBADUz60NehqlpSTzoEeOygFjo/XZtJtrdm4BbBZUHk8wRgODrtxx55WaZslGEtKHsx0pASIMgpgq9joU+w0nmKY80WgVJCaFkpbHSYMuwJ5s5FzEYoJF2e5jvYuux5mnaomk2Sc/ij0amXOefOlwk5qy72KTE2TU4ABYbJUuXFv7mCs5ClMlbKl2ZhDAY6gscQhGAytSomf/s61+PiNm8s8JhO67Ho8d35e2rGp1sImF81mnbSLEIgmcGF2EZd3L/np3rJbsEE8ebZwM5zQAJe7Id4ukKAAACAASURBVKXbboBZq8L3Xh0FgKL8vwym8Mh9h6aXxdZ12vQgBBh3V79gYwkQXXbD0jCJQHYBvFwBBgCLTlW0euQRiwp7jWPQgPwKHvP/Nho1K1IAB6JCA6GhwvNZvmlwp6Z8cAViFdsfAFEwiGQLBpVOJutpNCCepEX9zS/M+bG7wwKHWZtTAR51h6Td02IUYOYZLkYBXk0LxMCkLyuVqFbs77ZCQdbuQIwNWwA3m7VwBaJ4/PQskimKt+5uAwBpdSfnA66kACaE5F2Bl8PsYgTNptzNRdVgS7MJkXiqLOV62BkEpZAtgAkRtoRroQCzDOBqJQVI4e6hHAVwDnWz0agtPwZNHOW8kmxuNmHYFcxSWNhEsXLZ32XNm/2ZD0IIbt3uwCuX3JJ6WUsLBCBkATMLxKlJL1IUuKxnaVu4z2HCpiZjUT7gaV8EnmAs5wVJoSDY1W6BNxRHq0WH7TK7JbnY0WqGUkGkJrp0ZnzhDM+2TpzEOOYp38+fCxaD1G03SOOElyuAoVgyIwKNYdGri26CY+PI2bSwWmArogBmqTg3bmvG7GKk5pFX/kgCJq2q4vNZu1WPeX9UNjv62fPzUBDgpm2V5/az9ye9cTiVohhxl9c/w+gpcheDUorBOT+2t5iFHUyZAtgficMViKJfzOUuxgPMaoLePNd/g0YJjVKxalnAi5E4hl3BFSuATVoVdrRacHRsbSZBbNgC2GHWIp6k+PHhcfQ0GqQvQk+evMERVxAWnapsDxqbxlMtahmBxtjSnLs5qhCD88KFoq9FftXf396A87OLObe0hpwBPHyi9EEczkB1hmAwWPHmW9YIN7EQBiG5820bTRrZnYRCUCrmGK+CAhxLpLJUotkyMoCryS07HAjHk3jk5DSA2g3BYLSkjUpnW3uXdS0pwIQQ3N7fioND7qwM21SKYtgZwCMnp/HFx87jD398HACwpzN3RzazA928vbmkIkenVmJrsylLAU6lqPCeLftc1ioKbWknRJ9znHAwlpBVMC16ddEeYFZU1DQHuCgFOACjRokDvTakaPZApWrjjyQq8v8yWBTarC/buvP8hXlc1m2rir2EnS/TbQDTvjBiiVRZ4hGj2CzgKW8YwVgSfS1mbG42YsiZbWlkz8Gu+4U834CgGOvVyrwLcEKIkBok0zOyEpwRF8NyDbe14kCvDcfHvauefVwOG7gAFi4OA1M+vHV3m3Th6bQZoCC5FeBNTcayV+IdtuoWwMIUuNoWSVtF9TaXjyofg3MBqBQkZ2h4f7sFkXgq5xbVvz11EZ/62cmSo5ucVVZPrXo23jPzpDbpEbbQtCr5rcliO8qXsxhJIJZMragHGIA0dWnIlfl+TJcxBrmaXLO5EXq1Eo+cEgrglhp/5qVpcIEojo0tYHOzMUvBvr2/BYkUxTPnBRuEKxDFV58exNX/9Axu/dcX8P9+fBzfeXkY4VgSH76uF7vbc3dks4EYpdgfGP3tFpxetoviCkYRT1K0L1u05BqGcWrSiy8/cb7siLSJhRAMGiXsRk3OccKhaHYTHCDkvhabA8yK0ppaIExFKMCzfmxtMUsDXGptg/BH4hUlQDBy9aHM+yM4NenDLWV8/uSwy9gAmLWqkgK4rUEvxJQW2MVgw2G2iQqwLxzPej9ZAbxLXHwGisgCHisQgcawGzWSXWelGZgSFuwrpQADQiNcKJbE+Ro0tNea2oxTWgM40i6ib9vTJv23RqVAu1UvmwQx4griyt7yO2Q7rHp4gjGEY0noq+BPnfVFcN2WxsJ3rAC7UQOrQV1WFvDgfAC9TUaoczQ99KdNwlreKJdKURwcciOepPBHE1JofjG4ArGsGJ1KyBVuPrEQyun/BYRhGKyj3CBz8c8F8w03rrAFYgsrgOcDkhcwKI5PXU0FWKdW4vqtjXj63DxUClLTGCxgqcCeW4zg+IQXt+7I9kXu67Si1aLDTw5P4OCQGw+fmEYsmcIt25vx1t1t2NVuwbYWMzSqwhrDHXva4I8kcNvOlpKPtb+jAQ8cn8L8YkRqDlyKrctctHTbDZhbjCIST2b4uf/58fN45ZIbv3ltb1kNhhMe4XvACgMhSzfzuxKUiUEDhCzgczOZ900kU7j3pWG8/8ruDLWXFdXl2mmKwaxVQa0kedNbBuf9uHWHAx1p2boHanZEgj+10gY4IK0AXrbD8/wFYfz2LTKf83JYsowt/Q1HioxAy4dSQdBlK5wEwSLQtrWYJGV3yBnM6Klgft5SLBAjrqA02CcfQm786hTApyZ96LDqV7R/5Ao2EGNsYUWSJ6rJhlWA2fZyp00vKTCM3kZjVt5gJJ7EtC+c1/9TiGomQQSjCfijCbTWuDAhhOT0UTFyKUeX5gN5R7puaTZBo1JIk7DSuTDnly5CpYwbpZTCF45LJ+Fq0JCjs3fCE0anTAIEo5iOcjlWeggGgy12htOGYVQyBKOasItzs1lb82g4tjv0+ogHnmAMl8vEQikUBG/ub8HhUQ9+eWoG77uyC8/86U247yNX4e4ru7C7o6Go4hcQCvzfvK4350IxH+wCnu6lZ+9Z+7K4KWbvSrdBDDsDeOWSGwDKVnAmPOEMH7zNqIYnmDlJLyQTgwYIEYPLm+Cev+DElx6/gB8cHM243ROKSfGCtYIQIhbw8js3rkAUrkAM21rM0qJwusZRaIFooioKMEsLWn68z1+YR6tFJxvTVw7MRuFdVgAbNcqKrWndjYaCFogLc344zFpYDZqlRf2y69eoKwiHWSsdT6EmuGSKYsITRk9T4TQbYRDI6lgg8jXc1ooOqx49jQY8fGKqZoN2asWGLYBbLDpolAq8fW971pZGT2P2MAxhilJlWzjMg1WNAngpAq32RZKQDiBfAJ+dXsSezz6JU5OZMSiReBJj7mDeAlitVGBHq1m2Ee6VtBGWpTSSBWNJJFO0qgMkzFoVFCSzqSOaSGLOHymgAAsXglLHIS+NQV7ZAhjIjr2rJAO4mjBFutYNcOmvwbJ+L++R9+/+v1v78KX37sVrn74Nf//O3dLFdiXZJRXAS4vIXO+ZXBTajw+PS0205WRyU0rFYTBLxbbdqIUn47uSQjJF5RVgnRr+SCKjD+Cx08Lf/bGBzCbDhWCspg1wDHue5tUlddEMo1aFBr16BSwQCZiq4AHWqYUC9KETU/jnx8/j4RNTODeziJcuunDLjtL85/lgk/rSdwGGXUFsai7fPsjosReeaDg4F8D2VkGp7bDqoVUpsq5fbKCFVqWAUkEKeoBnfGHEkqmiZgBYDRpZBfjCrB+fe+RMWYlKxeALxTHmDq24CksIwW9dvwnHxr14fY1NhduwBbBeo8QDv3cd/uiNfVk/62k0wBuKZzS4MA/T5gpiXHJtQZXDXAXZrKWy1WGCKxCT/VI/dXYOgWgC//3CcMbto+4gUnRpElgu+tsbcGbal3VCe3XILV2YS+moZQ01pVgmCqFQEOGkltYEN7UQBqW5EyAAIQUCKD0UXSqAzStrgQCELUp5BXj1LBCAoGZe3m3F1iK2ICul0aSFggjZlmwAhhzNZi3uPtAl7RCsBhadGr2NhowkiBlfBFqVIqtZrHtZARyJJ/Hzo5O4vb8FDrMW52ZLT2RxB2MIxZIZC0G7QZ2xa8O2l2U9wOJClQ17iCdTePrcHExaFS7M+TOUO08oXlP/L0Pw7st/Z5m/lBVY7Va9tOCoFUITXHXcir99wyZoVQp868VhfPInJ/DWr74EfzSBm6sQf8bQq5XQqBTLFOBARRFojO5GIwLRRM5zaipFMTjvl76zCgXBpiZjVg/LiDuI3ibBtmPUKBEs4AFmqnO+CDSGzaCGNxTPuqb9+PA47ntltGZNk6fFRfBKK8AAcPeBLtiNGnzzhaEVf+1K2LAFMCDkaMplm7KmrXSzPfMw9RaxBZILh1mILKuGYlDrKXDp5NpGAoBXhwSl9rHTM5hcWFKW2IUinwIMyIf5x5MpHBp2SyNhS7EQsEVLtUcIW/XqDAV4QjzeLlseC4SpfAsEIbVt9snFFocJTn9UWkgwP2nLCuw0FOJ/P3Y1vvCu3TV/nfRs7fQBGPVKf3sDzqSNRGZNi8vVtkajBgaNUiqAHz89i4VQHL9xdQ+2t5rLUoDlogBtRk1GgcKGDMjGoImFHbNBHBxywxeO4y/eukM6RoagANf+O2FfdvzpXJjzw6JTSbsEHVYdpmpsgfBH4jBXwQMMAB+/cQse/6Mbcfbzb8Fjn7wB//a+ffjrt+2U9bmXCyEE9rRhGNFEEpML4Yp2TxksCi3XSOSJhRAi8RS2ty5dd7Y4TBkKcDCagNMfla7zRq2qoAWCeYaLUYBtBg0SKaF3JZ0TE8Iuaak7gsUijVxfBR+uXqPER67rxbPn53FupvrRprViQxfAuWAf8vRGuFFXEE0mbUVxNCqlAq0WXZUtECtYAM9nrqLDsSSOj3tx5z7BRvJ9McwfEBrgFKSwZUTOw3hywotgLIm37xWaE0tRgNmFtNoFcINhWQFcIAMYWFKAXSUmQbgCUdgMmrInJlUCa1JhF4zZxTCaTNqcSRcriUGjKmsYRzmwnZXLunPHl9UL/R0WTHjC0uJvJkdsHSFESIIQz2s/PDSG3kYDrt3ciJ1tFgzOB0qOMmILwfRJf41GDQLRhJQ3G4wxBTj7vWPfU7bgeuz0DIwaJX7tik5c3m3FowMz0n0XQrEVWRTajRp4cixaL876sb3VLC0u2hqqm+2+nFgihWgiVTUFmKFRKbCzzYJ3XdaJj92wuSz/eT6saeOQx92CfbCSBjgGU2BzNcKxRVx6U/WWJiPGPSHp88jU3N60ArhQE9yYOwSNSlGU4CQ1AaYtoqKJJM6K1zhnjQrg01M+dNsNNW0Szcc91/bCqFHiv9eQCswLYBnYyXzMlakAb6pA/WV02HJP4ymFOV8EZp2qpHSBcumyG6BRKrIU4KNjC4glU3jP5R146+5W/OTwhLSSvjTvR0+jsWDBsqPVAgUBzqZ5GF+55AYhwJt2tkCtJFkd5fmQLBBVLoBtyywQkwthqJUkrwVFr1HCoFGWrgCvwhAMxhZRsWeWn2lvZNX9v6sBU/jkGuDqDWmsuKgCz3hzDy5hUWgX5/x4fXQBH7i6GwoFwfYWM2KJlKR0FQtbCHam7YRI45DF7y3bXjbkGIQBCAvXZIriyTNzuGWHAzq1EnfsacOZ6UWp2FlJBdifVsAzKKW4OOfHtrTiqt2qhy8cl1UQKaV4dGAGsUT5+ajseauRArGS2NJ8sMMVDJD6/+2deZBjV5Xmv6t9TSmVUq6V6arM2uwq10YZu7CxyzZ4oTEE0IObxT1sY3a6A5gYoJuhoTumISZgCAigcTAQ0AM0SzdEA7bBNjbYZYz3pWxX1l6VtSj31L7rzh/v3acnpaSUlNKTnnR+EQpnKSX55U2l3nnnfuf7ShENh0qDcMfmVu88Tg26kOeF5yjdXPl87rSaEFsjCvn0QgyX+Bw1DeAK6ZF6EO6lC2Gk5YvL+TolEF+69wi+d+jUmo97/vxKW7q/Ao/DjLe9cgK/ev5iS/zGWwEVwGWwW4wY6rMWbbOcWow15Q94Q5PCMILhpCbyB0DaEt7kd66yQjt0YgEmA8MVG3147zWbEEll8fMnZwBIEohahoLsFiOmAq6iDvChEwvYOepBv9MiTdTWoaEVBXArJBBqH+CZ5TjGvPY1t8cHXJW3UyuxEE21ZQAOkAokk4EpFzvBUI8WwLIVmi46wGIX5bwUKjMbSVX8nYkC+IePnYHFaMBfvmIcQEHTWq8TxMxSHANOS5G8QXRpxfs+XqUDLLT64UQGj59awmIsraRy3rxDipy+5/BFJDM5xNI5ZcCqlVSKQ54NpxBOZksKYGE9t/oz/ckzy/jQD5/GfTVEZldCaKObMQSnJZITiLR+Bfng+s+fNrMRI57KiYbTwQjGvPainVpxHhK7WoVIY+l4XFZjTR3gWo/fq/ggF94/IlAHqF8C8Z/PXsAvn6keCLUcS2NmKaFpAEY53vvqTTAw4DsPn1z7wR0AFcAVuGTAqThBRJIZzEdSTRHxj3rtTYnPDIaSmsgfBFODzlUd4EdPLGLPuBdOqwl7J/qxb8KL7z16GqlsTvJMrJAAV8qO0UIkcjydxTNnl/GqzZK/cb2m4uEWdYC9DktRYtW5pXhV+YPA57TW/YG3GEu3rQA2Gw2YGHAUOsCh9oZgtIu37h/Hp27d3rbtxHrwu6wY7rPhxQshzEWSyOV5xaHFiQEHUtk8fvzEDF53+bBS7G0edMFoYHXrgGeW49hQ8ndQ6IBJf7dKB7jsEJysAU5kce/hi7CaDEogyLjPgV0bPLj7cFCRH2nRARZdtN88f7HofrUDhEAMNl8ok672nKz5XI9EQki6mi2BaDWSE4J07KfmY/C7LE1rSqhlPKUcnY2sOu+IxpUYhDuzEIffZVW66g5LdQlEPs9xejGGjTUMwAEFFwz1EOCzMysY8djgtBixEKnP1nM+ksLJMml2al6QrUR3tdmHd8Rjx5v2juHfnphpmda5mVABXIFLfA5FA3x6QfpvsyQQokuzHoLhpCYOEILNAVeRjiqczOCFcyt4lTyoBgDvvWYSZxbj+O4jp5HN8zUH4AQ7Rj0IhpNYiKbwxOllZHIcV09Jr+tz1tcBDicyYAxNGxoReB1mRFNZZOQLl5nlhJIEVQ2/09KQBELrEAw1k37J9zmayiKSzGLE214HiHawd6IfH7huqt2HUTM7x6REOOHxWimeW8i70tk83n7lJcr9NrMRm/xOvHyx3g5wokj/CxQK4MXSDnAZGzRRFK0k0rj3xSAObgsUdZNv3TmC52ZWlBO8Fhrg3eNeXDXpw3cePlUkg1AHLAiE13K5Ilf4m4t5jUYQEohmf561Gp/DgpWE5IQgElSbxSUDjrJDcNlcHifnY9hW4jzktJow4rEpDZzTi8VyRtcaQ3CzkSRS2XzFRNNSRFCPesfwmZll7J3wwu+21qUBFqmgkVS26vPE38eODgiiuPPaKaRz+aKZoE6FCuAKbPQ7MR9JIZ7O4tSi0DCtvwPcDCu0bC6P+UhKMwkEUNBRiYuBx08uIc9RlER3844hjHnt+NoDxwCgptQcoHgQ7tHjC7AYDUqSW3+dHeBQQpqYbnZYgle5qs8gJtvwjFcJwRDUK4FIpKWt3nZ1gAGp239mMa68R3uxA6w3Lhv14OR8VNnmrdgBlovVLYOuVamW24fdmJ6tfYI7m8vjwkpilROK0gGOiQ6wVFyU6wA7LZLH9h+PLmA2nFLkD4Jbd0oyiB8/fhaANh1gAPjw9ZsRDCfxi6cLW8/TwQj8LktRytagW7LMK1cAv9CMAliWQKxn+LodeB1m5PIc4WRW8gBuagEsnZtLu7anF+NI5/KrUkUB2d9c7gCfXowVFbNOq1FxKimHOOfV4gABSLuPjBV2QBaiKcwsJbBn3Au/y4qFOppfar3wyfnK+vwXzoWwccDRdOlfI2wedOHmy4bxgz+dWdNdo91QAVwBMW16ZjGOU/OxovvWQyEMo3GR+EI0jTzXxgFCUGqF9uiJRVhNhiKNpMlowLtetRGJjPRhMjVY2weG2sz/keML2DvhVaKifQ1ogFvhyyq2wkOJNGZku7dqIRgCn9OKxVhq1fbVn08uFkkqBGLbKNDOAtjvQjqXx+OnpISwdnsAE2uzc7QPeQ48OD0HABit8Dvb0O/AJr8THzw4tcombfuwGzNLiZpPWhdDSWTzfJUUyCMXAOLCTwwYlRvkMhgY3DYzHjm+ALOR4YZLi+24NvqduGykDw/JP1ept3GruGazH7s2ePCtP5xQ5GpH56JF8gegsrNPNJVVhr9my8gjaiWSkj4jXDqTQIgu6MxSHAvR5sgHBaV+1oJjcoe+tAMMAJMBJ07ORRFPZzEbThXJGZyW6h3gM4v1nf+NBgaP3awUwM/K+t+9E/0IuOqTxKkL4GpprC8Hw8owbCfwwYNT2D3ubVskdK00XAAzxv4vY+xPjLG/b+YBdQqX+GQv4MUYTi1EMea1N8WCabQJ8ZlaegALJgOyjmpOFMALuGKjb5U91u2vHIfTYsSGfnvNDhVehwUb+u04dHwBL10MK/6/gNTxWUlkipKiqhFOZltyFey1i3z7DGaWZA/gGjTAfpcFmZzUCRFMByO4/a7Hyk72tjMEQyAuXB6R0/ioA9z5iK3PP0zPw2ExKtraUiwmAx785EG8ed+GVd/bNixdiNaqAxYXgqUSCJPRAI+9MAQVT2XBGGAzlz/diGO9ZrO/bIDNrTuHIf78+zXSZDPG8KGDUzizGMfdh4NSwEKJA4Rg1GtX/LIFL54PgXNJD9qcDrDOCmA5se/ps1IyWLMlEMBqJ4jp2QgYkzqQpUwFXIiksnjqjHQ86oE2p9WEdDavyNtKOb0Yh9nIVkWLV0Mdh/zszAqMBoadox743Za6JBDqYrlSBziezuLsUlwZZO0Edo978YP3vLImmWA7aagAZoy9GYCRc34AwCRjbHWcms6ZUHeAF+PrCsBQY7cYMeC0FAU/1EswpJ0HsMBhMWHMa8eJ+SgWoikcCUZwQCV/EPTZzPift12G9187Wdfr7xjtw6Hji+AcRQWwz2EG5yjbLS1HKJFpagqcQC2BUDyAq4RgCISWVy2D+O4jUuH7UpkI6AVZLyw8hNuBSDv80wnJjk5LrTnRGKMeG/odZsTSubIhGLWwXT6B1loAnxMXgmVOcurh1Vg6B6fFVPGYxAVrqfxBcOvlhfu9Gqbu3XTZMKYCTnzzweM4v5JAPJ2rWABfKEmDE/KHG7YPYS68egeoVsSFs95s0MSO2dNywSkaKM1ANKfOljhBHJuNYsLnUHYP1Yj//wMvSzsJGweKC2AAiFdIgwuGEhj22OoKxJHS4KT3/zMzy7h0xA27xYiAy4aVeKZisV2K6ACPeGyr4pwFR2ej4BwdVQDrhUY7wAcB/FT++ncArmnK0XQQHrsZPqcFpxdjODUfbeoV7Fj/+qzQZsPaxSCrmQw4cXw+isdOSlvjrypTAAPA7VdM4I4DG+t6bbF947KasFtl5dKvWBLVdtUcSmRa0gEWnaeVuCSBcFiMNW3H+uRCdlG+kl+MpvCLZyVd4fTs6kKj0AFuXwHc77TA57QgnMzC77LCYiKlVKfDGMNOuQtcT6dKzYZ+uxRBXGMk8sxyHAaGsp7DPkchTCKezsJRpigR9NnMMBoYXnvZUNnvbx50YeuQC26bqemBDdUwGBg+dHAzjgQj+JZs7q9OGBOMeG24uJJEXrVLdfh8CEN9Vuwc60M6l6/bClEQTWVhMRo0C4BpFmJY8emzK2Bs9S7BevA4zPDYzbj3cLDoPDo9G6k4dyIkfA8ckSzpJgbUQ3DS2kbT5WUQK4lM3TsPkn2ntHP53EwIe8YlqaDY2at1MHo+moLJwLBvor8ool7NETl5bTsVwHXT6KeJE4CYDlgCUPTJxRi7kzH2JGPsyfn5+fUcX1u5ZMCBZ86uIJzMNlXDNOqx4/xy4xrgYDgJs5FhQCM9nGAq4MKJuRgOHV+A22pqqum2GIS7cpOvKAGt4MlZWwc43KIC2FPUAU5gvN9RU5dN/I5EZ/eHfz6LdDaP23aP4uxSXJmQF4gBCa1/t6WI1CaSP+gHoaVv9HfGGMPWIRderrEDfHYpjhGPvWxR2u+0FNmglYtBFly3NYB3XjlRdcDtYzduwTuvuqTi91vFG/aMYsxrx4/+LA3hbS5TYI157Ujn8kWJjy+cD+HyMa8iU2tUBhFJZnSn/wUKDYOzS/GmyQfVfPLmbXjxQhg3fvkhfPX+owglMji9ECt7gQJIckGHxYiZpQQGnJaiXUIh1atkhdZIU8UrB4EIN52949LAqRhurjUMYz4iecJPDbowo3JhUnMkGIHDYqxpJoUoptECOApAtBlcpa/DOb+Lc76fc74/EAis5/jayiU+h2IM3wwLNMFYvx0XVpINb4vNhpIYdNua7nSwFpsHXUhkcrj7hSCunPQ1Nar38g0emI0MB0sy6fsd5U3pKxFKZJruAQxINkRGA8NKIo1zy/GaHCCAwgfeUiyNVDaHf33sDK7bGsBfXD4CzqXtKzWLsTTcNu0ifyshOiZUAOuHnfIuynqGFreP9GE6GKnps2lmKV6xszfgtBQFYVTrAL//uil8/o07q/6/Xr9rFP/jlu1rHlOzMRsN+MB1kpxrxGMrWwiVznWIAbjLxzyKTG22wQI4mszqTv4ASJplcXpq5u6p4I6rLsEDn7gON146hK/efwwH//eDyOZ5WYkKIHXzxXGUBlqI9a00CBeK118A9zvMWIqnlQG4PfKweEDe2at1EG4hmkLAbcVUwFmUZqdmOihp07WuB7qBRiuYp1CQPewGcLopR9NhqK1SmtkBHvPakcjkiqIS6+FiKImhPu23yEVRFEpkcGDKv8aj62PQbcMDHz+It79youj+UlP9aiQzOaSy+ZZ0gBljUhqcrAGuVdwvhkEWoyn8+rmLmI+k8J5rNqn0lsXbzfPRVFsdIARCM0cOEPphz7gXBrY+veX2YTdCiQxmw9VP0KlsDtPBSEWnF9EB5pwjmsrCqUFke6v4L/vH4XdZcdlIX9nvC8mJSIMTA3CXb+hTCuBgqDHf90gyq7sBOEAqOIUOeLIFBTAgOZp84+378JM7r8KIxw4DQ9VdSXH+KnVzWEsD3EgHuN9pQTKTx59OLsJjN2OTXEuIz/ZaB+GkDrBFmcso1QFzznEkGCb5Q4M0+pf1SwAPM8ZGAdwK4KrmHVLnIAbfjAZWlHW/XhQrtOVEQ7Y+s+Ekto9o/4ZXn+wq6X/Xw0QZm5lKsaTlEKlJregAA5IM4vRCDLF0riYHCACwmoxw20xYiKZwz+EgNg+6cO0WPzgH7GbjqujZdodgCKgDrD/GfQ789m+vxWQNEeSVEBZSR4LhqkO2jx5fRCydw42XltftDjgl95NIKot4OqeZYjPobQAAHdRJREFUfVkrsJmN+PkHDlTclRGhI0KPKgbgdo554HNYYGDrkECk9NkBBqSBxaVYuiUdYDVXTg7gVx+9BsFwUvHZL4e4MCz18xUBLeU6wJxzrCQydQ9fisf/4eg8do97le5sIxKIHaN92CRcmEqcIOYjKSzHMzQA1yANdYA552FIg3CPAbiecx5q5kF1ChPytOmEz9HU4QslDKMBL2DOueYpcIKAy4o+mwk+p6Ws12IrsJmNcFiMNXkBKzHILeqY9DssysmtFgcIgd9lxf0vz+Gli2G85+pNYIzBYGDYOuxeNXG/EE21NQRDsGOsDxajAZdW6HoRncmWIXdd0+qlbJet0EovzEq593AQbqup4oVwIQ0rjVgqW1UDrAc2+p0VLwg8djMcFqMigRADcINuG0xGA/wua8NewNFkVnchGAIxCLdpHRdktWI0sKrFL1C4qC+VQDiraICjqSxyeV53B9inku7tHS945dstRrisppokEPk8x2IsjYBbim0e7rOtskITf6dUADdGw59KnPNlFJwguhJhlt3sK9hCAVz/h6LoqLSjM8cYw8Ftg/A5LZrqjfodtaXBCau0VqXheO1mRGRbolo7wIDUxX7qzDL6HWa8ed+Ycv/2ITfuf3m26LGLsXRHFMAjHjue+uxrdHvyJRrD4zBjxGOraoWWy3Pc9/Isrt8+uMoHXKCOQ46nc3BW0QDrHcYkj9gLqg7w5WOFomfYY1tHBzgDt02fxU2rJRD1cmBqADdsH8RVk76i+8XFWayMC4Q4p3jt9e1geFWuEXtUYVGA5A2/UIMLxHI8jVyeK+eDyYATJxeKJRDi71RcuBL1Qf5GVfA5LRj12BR7oWbhdUgdg0bikEUnoV3erF972178wxt2aPr/9DlrS4MLJ6QPsFYVwOqEuXoKYOHo8PYrJ4q2UbcNu7EYSyvbYZlcHivxTEcUwID+4leJ5rB92F21A/zE6SUsxdK4RY4pLoc6DjmWytYciqNXRr12XAwligbgBEN9tnUNwelRAwwAPqcZFqOhYVu+ZuN3WfHdd12BQXfxuVNITGJlNMAr8cZkdWL2AwD2bCgtgK2Yj6z9fhA6YTE4Nxlw4sRctGhA9UgwgkG3VdcSo3aiz78sjWCM4Z6/ubassfZ6X3fMa29IAtGOFLh20++0YKmGgUFxtd4qDbDY1u13mOvS5Q312WAyMPx1iTeyOngg4LYq3pCdoAEmepdtw3145PhJZHL5stKv374YhMVkwHVbKzv8rOoAW7u3AwxIQSQvXQgXDcAJhvtseOL0Ut2vyTlHRKcuEADw1wc24spNA+uS5GiBzWyAgZWXQAhZXb0aYHGu2OR3rrL3C7itODZXOdZYsBCRzgdicG7S70I4mS3aJTwSDJP8YR1QB3gNPA5zS4IARr2NhWG0IwWu3fgc5po6wFpIIID6ur+AlIv+w/dduaprLz64jshOEEoIRod0gIneZPuwG5kcx6kyxvucc/zuxVlcuyVQVdcrTvqzoSSyed4THeCFaApPydG/6l3DYY+U/pXMlHcZqEQqm0c2z3W7E7NzzIO3vGJ15HanwRiD02IqOwS30mABLB6v1v8K/C5rTRrg+ah0rld3gIFCJHI2l8exuSg5QKwDKoDbhPACrpd2pcC1k36Vp2g1wq0ugOWTer2G46NeO66cXD0sNOCywu+yKtvNhS0v6gAT7UM4zJSTQRw+H8b5lQRu3lHe/UHgtBhhMRmUyPdu1gADBSu03704i+E+W9E2u/isDtY5CCdcbfQYhKE3nFZT2Q5wo00Vq8mIj924BXccWB3e4ndZsRLPIJ2tHocspHEiFVQM8QkrtNOLcaSzeWwj/W/DUAHcJsa8dizF0quSwNbiQigJr8Pc9qAELfE5LIimsmVTcNSEEhk4LMaWxaWKDvCGGkMwamG7yglCSCCoA0y0k0m/C2Yjw0NH5lZ9794XL8JoYHhNBfszAWMMPocFM3LipUOn2/i1IqzQnp1ZWTUz0mgaXFQeuHV3+dp1Ak6rEfF0ZQ1wvUNwAPDx127F3on+VfeLju5irHoXeCGahtVkUH7/o147rCaDEolcGICjDnCjUAHcJoSv8IU6ZRAn5qIdM1WrFWI7dWUNHXAokSmKuGw2YlurmZGT24bdODobQS7PlW2xASqAiTZiMRnw3msm8R/PnMd/PH2u6Hu/fXEWV27yVY0tFvQ7CwWwXnWstTKqCowpDWMY9kh/z/UOwgnHGb0OwekJp7W8BCKUyMBiNMBmbl6p5JdnPITGtxLzESkFjjFJQ22U0+xEB/hIMAyjgWHzYOtt5roVKoDbhEiZe/rMSs3P4Zzj6GykYtxjtzJQYxhGOFl/Yk89TAVccFlN2FNG19Uo24bdSGXzOLMYw0IkBZvZ0PXbxUTn88mbtuLKTT585hcv4OWLkkb9+FwUx+eiVd0f1Aw4Lbgoy7yqRSF3A+qZDPUAHNC4BEIUZN1+8dAJOC2VJBBpeBxmpQhtBkLSIDS+lZBS4IqbIZMBpxKGcSQYwcYBR0/tBjcbKoDbxO4NHlw20od/+cMJ5PJ87SdA2hJZjmewpccK4H6VpVI1GomsrIdRrx2HP39zU23x1E4QIgSjmR+2BNEIJqMBX3/7XvTZzPjg/3sKoUQGv30xCAC46bLaCuB+pwVZ+bNN70EYa2EzG5VipfTzwW0zw2kx1i2BKHSA9TkEpycqdYBX4s0/pwhXh7U6wAvRlCKXEEz6XTi7JGl/p4MR8v9dJ1QAtwnGGD56w2acXIjh189fqOk5x2Ylzc/Wod7a8lDikNcIwwglsuiz6+tEu2XQDQOTruY7JQSDIABg0G3DN9+xD+eWE/jkz57DvYeD2DPurdmBZkAlk+j2DjAAjHltqwbgBEOe+r2AI/IQHEkgWo+rggY4lMgosx/NIqB0gKtrgIUEQs1kwIlcnmM6GMHZpThZoK0TKoDbyM07hrF1yIVvPHgc+Rq6wEeVAri33vTqWNVqhBOZlnkAtwq7xYiNA05MByNlt7wIop3s3+jDZ153Ke57aRYvnA/h5h21dX+Bwt8tUIib7WbuOLARH75+quz3hvtsDUsgqABuPY4KLhCt6ADbzEa4rSbF5aEc2VweS/G00i0WTMpOEPccvgiABuDWCxXAbcRgYPjw9ZtxdDaqbC9W4+hcFB67GYPu3iqSxPDZUqz6EFy4xRKIVrFt2I3p2QgWomllQIIgOoV3X70Rr981AsZQs/4XkJLABI4uD8IAgL98xQbcURJ2Ixjus2E2vLb3qxohgeh2+Ugn4KoyBOep0wO4Fvzu6l7AS7E0OC/ohQXCC/juF0QBTBKI9UAFcJt5/a5RTPqd+NrvjxdFHJbj2GwEW4dcPacRNRsN6LOZsFxFApHLc0RS2Za6QLSKbcNunF6MYSlGHWCi82CM4ctv3Y3//PA12FSHA43PWXgv90IHuBrDsgSilp0+QTSVhd3cOltHooDTYpKCR3LF3rySBKL5TQm/y1K1Azwnf6+0A9xnMyPgtuL0YhwOi1FxkyIag/6y2ozRwPCh6zfj5Yth3P/yat9NAeeS7qfXBuAEvjXCMIReTo8d4O3DbnAO5DmoA0x0JFaTEZdvqG/4s1/VAbb3+KT6sMeGbJ5jsYZAH0EkmaEQDI0QUd0xlQ44k8sjmsq25JwSWKMDXAhFWt0QETaoW4fcMHR4zHSnQwVwB/DGPaMY99nx9d8fq9gFnoukEE5msbVHPf/WSoNrdQxyK1En+ZRueRGEXhHDq06LsedP1MIKrZ5BuEgySyEYGiFkJmodcLjBGORakOKQK5/PFip0gIGCDpj0v+uHCuAOwGw04EMHN+P5cyH84eh82cf06gCcwOeorQDW2xAcAEz4HIrR+oCTCmCiOxAFcLenwNXCcANewNFUlgbgNKJcAdzKporfZUUokamYbio6wH736h3BKVkHTAXw+qECuEN4y74NGPXY8C9/OFH2+0dnpfSXrT36pu93WqpqgPXcATYamHJhEyjzgUcQekS4QFCwSyEoox4v4EgySxIIjXCVkUCsiHNKCzrAShxyhS7wfCQFl9UERxnt/KUj0o7h5RuaF8jUq1AB3CFYTAa85RUb8PipJayUKfSOzUbgc1p6dkhqQJZAVJKIhBPSlbseC2AA2CYXwL36+yW6DzG8Wu4k3mv4XVYYDawuCUQ0mYXbqs/PM70h3qNadoABVNQBS5aY5Zshr5oawG8+dg1ecUl/04+r16ACuIM4uG0QeQ48fGxh1femZyPY0qP6X0DqAKeyeSQy5beMChIIfZ5sX7drBK+5dFC3BTxBlMPntCgDRr2M0cAQcFlxsUQCsRBN4eov/r6s9I2G4LRDxE2rrdBCcVkD3JICWCpuKzlBlEuBEzDGsGO0eWmkvUxDBTBjbIgx9nCzD6bX2TPuhddhxoPTxW4QnHMcn432rP4XkDTAACrqgPUsgQCA67cN4jv/9Yqes7gjupvNg25M+Gq3TutmyqXB/ftT53B+JYE/nVhc9fgIaYA1o5wGWOzEtsoFAqjeAa5UABPNo+6/LsZYP4DvA6BPtSZjNDBcuyWAPx6dRz7Plcnpi6EkIqlsz+p/AakDDADLsQw2lNn5CSczMBtZz9stEUQn8c137ANd00kM91lxcj6m/Jtzjp88MQMAODkfLXpsPs+lITgaINSEcjZooRbK6goSiMoa4Gs2+5v+/yWKaaQDnANwO4Bwk4+FAHBwWwAL0TQOXwgp9ykOED0sgRCpUksVBuFCiQz6bGbqoBJEB2ExGSjIQWa4z1Y0BPf4qSWcXIjBbjbiREkBHM/kwDng1mGwjx5xltEAryTScFlNMLXg/VstDjmVzSGczNI8iAas+ZtljH2bMfaQuAH4W855aI3n3MkYe5Ix9uT8fHlbL6I8124NgDHgoenCuh0TDhA9LIEQE+XLVSQQepU/EATR/Qx5bIgks4inpSLr356Ygdtqwu1XjOPsUhwZVQqZCPYhDbA2OCxGMLZ6CK6V55SA26rYnakRXWGSQLSeNQtgzvn7OecHVbcv1PCcuzjn+znn+wOBQHOOtEfwu6zYNebBQyod8PRsBH6XVZEB9CLCU7RSklI4kdGlBzBBEL2B2gs4FM/g7hcu4o17R7FzzINMjmNmKa48NpqUCjEXSSA0gTEGp8W0agiuFSEYAr/LqgReqBFdYSqAWw/tTXUg120bxDMzK0q389hsBFuHelf+AEgZ6AZWuQMcpg4wQRAdjFIAh5P45bPnkcrm8VdXTGBSDjZQ64MjciFGQ3Da4bQaEU+pNcCtPaf43ZbyHWC5ACYJROuhArgDuX5bAJwDfzwmDcMdm+ttBwgAMBgY+h2W6hpgKoAJguhQhjyFOOQfP34Wl495sHPMgym/1NxQ64AjSSqAtcZpMSGaVmuAW9sBDlTqAEepA6wVDRfAnPODTTwOQsWuDV70O8x4aHoe51cSiKdzPV8AA3IaXKUOcDILj049gAmC6H5EB/h3L87iSDCC268YByAljfldlqIOcFQpgOmiXiucVpOmGmC/y4pwMrsqDllIIAYqBGEQzYM6wB2I0cBw3VbJDm06KDtA9LgEApB0wOV8gDnnNARHEERH47Sa4LaacM/hIOxmI964Z1T53mTAVdIBlofgSAOsGWoJBOccoXgGHnvritCCF3DxOW0hmoLXYYbVRJaerYYK4A7l4LZBLMbS+PenzwEAtlAHGD6HBctlJBCxdA65PEcfdUsIguhghmUZxOt3jRR1d6cCzqICOEoaYM1RD8ElMjmkc/mWd4ABrJJBSDHIJH/QAiqAOxRhh3bvi0EM9VmpuwlJArEUy6y6P6zzFDiCIHoDUQD/1SvHi+6fCriwHM8oO1zhZBaMFfxpidbjtJoQkzXAIlm0pS4QFdLg5iMpBKgA1gQqgDsUn9OC3Ru84Ly3/X/V+JxmLMfT4JwX3a/3GGSCIHqDvRP9uGJjP/ZNFMdZTgUkiZtIhIsms3BZTEoaKNF61BrglXjrzylCAlEahrEQpRhkraACuIO5ftsgACqABf0OC3J5jnAyW3S/KIDJBYIgiE7m46/dip++/8CqxMpSK7RIMkMhGBrjshoRkzXASge4heeUAdnbvlwHmCQQ2kAFcAdz46VSAXzZSF+bj6QzEGEYpU4QJIEgCEIvlItr39DvgMVoUHTA0VSWBuA0xmExIZGR5kmUDnALJRA2sxF9NhMOHV9EWB56jKeziKVz1AHWCCqAO5idYx787AMH8AbVtHAv018hDY4kEARB6BmjgWGj34ETcgc4msrSAJzGiAuOWDqrWVPlozdswZ9PLeKW//NHHDq+gIUIxSBrCf2FdThXbPS1+xA6Bp+jfAdYkUCQCwRBEDplKuBSbC8lX3P6PNMSpyiAU1msJKRzjNfRWi/e/3btJPZv7Mcnfvoc3vGdP+PVW/wAqADWCuoAE7pBSCBK0+DExDR1TAiC0CuTASfOLsWRyeURTWbo80xjnFbJdzeWyiGUyMBoYHBaWu/Fu3eiH7/52Kvx7qs34uFjCwAAP4VgaAL9hRG6QUggSsMwwokM3FaamCYIQr9MBVzI5jnOLMYRSWbhJg2wpgjLuVgqi5V4Bl67uaxeuxXYLUZ87rYduOmyYTw4PUeD7xpBHWBCNzgtRox6bHji1FLR/aFEhhwgCILQNZMqKzTSAGuPWgLRrmTRA1MD+MzrLoXZSKWZFtAqE7qBMYbX7x7FH4/NY0UlgwhTDDJBEDpHWKEdnY0gns7BZaXPNC0RQ3BRUQC30AGC6AyoACZ0xW27RpHJcdx7OKjc166rdYIgiGbRZzMj4LbiuXMhADTToDUOWQMcT+ewEqdzSi9ABTChK3aO9WGT34lfPX9BuS+UyJADBEEQumcq4MRzMysAQEEYGlPaAW5lCAbRGVABTOgKxhhu2zWCP51YxFwkCQAIJ+lqnSAI/TMZcGFOjsbtowJYU4ps0OJpOqf0AFQAE7rjtt2jyHPg7ucvAgDptQiC6Aqm5EE4AKQB1hiHWZJARJJZRFJZeFrsAUy0HyqACd2xZciN7cNu/Or5i0hlc0hm8nS1ThCE7pmSB+EAkkBojcHA4LAYcTGUBOcgCUQPQAUwoUtu2z2Kp84s46ULYQC0XUgQhP5Rd4BpCE57nFYTLqwkALQ+BploP1QAE7rktl2jAIAf/fksAJAPMEEQumfUa4fVJJ2WKQhDe1xWEy6EpALYS7K6rqeuApgx5mGM3cMY+x1j7BeMMRLJEG1hYsCBPeNexQ2CrtYJgtA7RgPDJr8kg3CTs43mOK1GXFyRhqvpnNL91NsBfgeAr3DObwIQBHBL8w+JIGrjtt2jSGbyAKgDTBBEdzAVcMFoYLCZaYNWaxwWE9I56ZxCHeDup66/MM75Nznn98n/DACYa/4hEURtvH7XCERUO12tEwTRDdy8cxi37BwGEx9uhGa4VLITaqp0P1VFRoyxbwPYprrr95zzLzDGDgDo55w/VuF5dwK4EwAmJiaadawEUcRQnw1XbvLhsZNLVAATBNEVvGH3KN6we7Tdh9GTOFUFMJ1Tup+qBTDn/P2l9zHGfAC+DuAtVZ53F4C7AGD//v18ncdIEBV5z9WbkMjkybKGIAiCWBcuOQ7ZbjbCajK2+WiIVlPXmKk89PYzAJ/mnJ9pzSERRO3ctGMYN+0YbvdhEARBEDrHYZFKItL/9gb1quzfC2AfgL9jjD3EGLu9BcdEEARBEAShKUICQfKH3qCuDjDn/FsAvtWiYyEIgiAIgmgLQgJBBXBvQD4rBEEQBEH0PCSB6C2oACYIgiAIoudxkQSip6ACmCAIgiCInkdogL0OCrntBagAJgiCIAii53GSBrinoAKYIAiCIIiex2khCUQvQQUwQRAEQRA9z4jXBovJgKmAq92HQmhAXTZoBEEQBEEQ3cig24bnP3cTbGZKgesFqANMEARBEAQBUPHbQ1ABTBAEQRAEQfQUVAATBEEQBEEQPQUVwARBEARBEERPQQUwQRAEQRAE0VNQAUwQBEEQBEH0FIxz3tr/AWPzAM5UeYgHQKgJ/6tufR0AmABwtgmv02k/W6e9TrPWGei8n63TXqfT3tPNfK1Oex1aa+1ep9PWupt/Z9261p34O9PbWl/COQ+s+Sqc87beANxFr7Pma8130jF18es0ZZ079GfrtNfpqPd0h64RrbX+Xqej1rrLf2ddudYd+jvryrXuBAnEr+h11mSlSa/TaT9bp71Os9YZ6LyfrdNep9Pe0818rU57HVpr7V6n09a6m39n3brWnfg768q1brkEglg/jLEnOef7230c3Q6ts3bQWmsHrbV20FprB621dnTrWndCB5hYm7vafQA9Aq2zdtBaawettXbQWmsHrbV2dOVaUweYIAiCIAiC6CmoA0wQBEEQBEH0FFQAtxnG2BBj7GH5632MsfsZY4cYY5+Q7xtjjJ1jjD0k3wIlz32mXceuNxpZa8bYJsbYbxhjDzPGvtzen0A/rLXWqsf9ijG2p+S+nYyx+7Q8Xj3TyFpXexxRmRo+Qz6v+vw4whj7tOq59L6ug0bWmt7XjVHDWk8yxh5gjD3LGPtsyXP1+75ult0G3Rqy8ugHcC+Ap+V/HwIwDoABeBTAJgBvBvDBCs//VwBH2v1z6OHW6FoD+CmAq+SvfwLgYLt/lk6/1bLW8v3vAPDVkucyAL8D8FC7fw493Bpd60qPo9v611r1+J8DGJO/pve1BmtN7+vWrDWArwC4Wv7+IwAC8te6fl9TB7i95ADcDiAs/9vHOZ/h0jtrEUAfgKsAvI8x9jRj7H+JJzLGbgAQAxDU+Jj1SqNrvRXA0/LXc5AMuInqrLnWjDEfgC8DWGaMXa967rsBPKjp0eqbRte63PufqE4tnyEAAMbYFQDOcc7Py3fR+7o+Gl1rel/XTy1rvQhgF2NsCIAVBVs0Xb+vTe0+gF6Gcx4GAMaYuOsQY+wjAJYAbATwPAAfgH8EEAdwP2NsF4AjAD4L4E0AfqntUeuTdaz1zwF8jjH2GIBbAHwaRFVqXOsvAPgZgG8D+GfGmBtS5+GdAG6Wb8QarGetyzyOqEKNay34GwCfkx8/AHpf10Wja73G44gy1LjWJgAfA7ABwO8BZLvhfU0d4M7i/ZCK248A+JJ8BfYo5zzCOc8BeAbAFgCfAvBNznkzgxt6jZrWmnP+TwDuAfA+AN/nnEfbdsT6pdxa7wXwDc55EJLM5CCALwL4NOc8064D7QJqXetyjyPqo+waMsa8AAY55yfkx9H7ev3Uutb0vl4/5dbwUwDexTn/OwB2AK9FF7yvqQDuIOTCa1r+5w/l//6WMTbCGHMAuAnAYQCvAfBhxthDAPYwxr6j+cHqnDrWGgCehZSF/hVtj7I7qLDWxwFMyl/vB3AGwHUAvqR6X/+TlsfZDdS61hUeR9RBlTV8I4C7Vf+m9/U6qXWt6X29fiqs4SYA44wxG4B9ADi64X3dbhEy3TigEpAD+D6AV6v+fT2kq7HnAXyk2nPp1pq1BvB5AHe0+9j1dltjrUchnbgOAbgPgLvSc+nWmrUufRzd1r/W8n0/ArBvrefSrTVrTe/r5q81gL8AcBJABMCPARgrPVdPNwrCIAiCIAiCIHoKkkAQBEEQBEEQPQUVwARBEARBEERPQQUwQRAEQRAE0VNQAUwQBEEQBEH0FFQAEwRBtAnG2D8wxg5W+N4extgejQ+JIAiiJ6ACmCAIojPZI98IgiCIJkNRyARBEBrCGOuHFE1sBMAAPMkYuxeAE8Bxzvm7GWP/DCnqHIyxOzjnN8oBLT8AMAjgBc75h9vzExAEQegf6gATBEFoy50Afs05vx5ABsAIgK9DSnjcyBgb4px/GlLU6Bc55zeqnneYc34tgBHG2K42HDtBEERXQAUwQRCEtmwC8Jz89ZOQiuD3QYod9QGwV3jeNgBvkqNHJwGMtfYwCYIguhcqgAmCILTlLIAd8td7ALwXwM8BvA1ATPW4BAAHADDGGIBpAF/lnB8E8Pfy6xAEQRANQFHIBEEQGsIY80PSADMAZgC/BfBWAMuQdMH/nXN+iDHmA/BTSB3hTwN4CsD3AAwDCAN4O+c8rP1PQBAEoX+oACYIgiAIgiB6CpJAEARBEARBED0FFcAEQRAEQRBET0EFMEEQBEEQBNFTUAFMEARBEARB9BRUABMEQRAEQRA9BRXABEEQBEEQRE9BBTBBEARBEATRU/x/EbiGB9apX8YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the RGNP data to replicate Hamilton\n",
    "dta = pd.read_stata('https://www.stata-press.com/data/r14/rgnp.dta').iloc[1:]\n",
    "dta.index = pd.DatetimeIndex(dta.date, freq='QS')\n",
    "dta_hamilton = dta.rgnp\n",
    "\n",
    "# Plot the data\n",
    "dta_hamilton.plot(title='Growth rate of Real GNP', figsize=(12,3))\n",
    "\n",
    "# Fit the model\n",
    "mod_hamilton = sm.tsa.MarkovAutoregression(dta_hamilton, k_regimes=2, order=4, switching_ar=False)\n",
    "res_hamilton = mod_hamilton.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>rgnp</td>         <th>  No. Observations:  </th>    <td>131</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovAutoregression</td> <th>  Log Likelihood     </th> <td>-181.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 24 Dec 2019</td>   <th>  AIC                </th>  <td>380.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>14:58:45</td>       <th>  BIC                </th>  <td>406.404</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>               <td>04-01-1951</td>      <th>  HQIC               </th>  <td>391.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                     <td>- 10-01-1984</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>approx</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.3588</td> <td>    0.265</td> <td>   -1.356</td> <td> 0.175</td> <td>   -0.877</td> <td>    0.160</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    1.1635</td> <td>    0.075</td> <td>   15.614</td> <td> 0.000</td> <td>    1.017</td> <td>    1.310</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.5914</td> <td>    0.103</td> <td>    5.761</td> <td> 0.000</td> <td>    0.390</td> <td>    0.793</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>  <td>    0.0135</td> <td>    0.120</td> <td>    0.112</td> <td> 0.911</td> <td>   -0.222</td> <td>    0.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2</th>  <td>   -0.0575</td> <td>    0.138</td> <td>   -0.418</td> <td> 0.676</td> <td>   -0.327</td> <td>    0.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3</th>  <td>   -0.2470</td> <td>    0.107</td> <td>   -2.310</td> <td> 0.021</td> <td>   -0.457</td> <td>   -0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4</th>  <td>   -0.2129</td> <td>    0.111</td> <td>   -1.926</td> <td> 0.054</td> <td>   -0.430</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7547</td> <td>    0.097</td> <td>    7.819</td> <td> 0.000</td> <td>    0.565</td> <td>    0.944</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0959</td> <td>    0.038</td> <td>    2.542</td> <td> 0.011</td> <td>    0.022</td> <td>    0.170</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                         Markov Switching Model Results                         \n",
       "================================================================================\n",
       "Dep. Variable:                     rgnp   No. Observations:                  131\n",
       "Model:             MarkovAutoregression   Log Likelihood                -181.263\n",
       "Date:                  Tue, 24 Dec 2019   AIC                            380.527\n",
       "Time:                          14:58:45   BIC                            406.404\n",
       "Sample:                      04-01-1951   HQIC                           391.042\n",
       "                           - 10-01-1984                                         \n",
       "Covariance Type:                 approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.3588      0.265     -1.356      0.175      -0.877       0.160\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.1635      0.075     15.614      0.000       1.017       1.310\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.5914      0.103      5.761      0.000       0.390       0.793\n",
       "ar.L1          0.0135      0.120      0.112      0.911      -0.222       0.249\n",
       "ar.L2         -0.0575      0.138     -0.418      0.676      -0.327       0.212\n",
       "ar.L3         -0.2470      0.107     -2.310      0.021      -0.457      -0.037\n",
       "ar.L4         -0.2129      0.111     -1.926      0.054      -0.430       0.004\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7547      0.097      7.819      0.000       0.565       0.944\n",
       "p[1->0]        0.0959      0.038      2.542      0.011       0.022       0.170\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_hamilton.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the filtered and smoothed probabilities of a recession. Filtered refers to an estimate of the probability at time $t$ based on data up to and including time $t$ (but excluding time $t+1, ..., T$). Smoothed refers to an estimate of the probability at time $t$ using all the data in the sample.\n",
    "\n",
    "For reference, the shaded periods represent the NBER recessions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, figsize=(7,7))\n",
    "ax = axes[0]\n",
    "ax.plot(res_hamilton.filtered_marginal_probabilities[0])\n",
    "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n",
    "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n",
    "ax.set(title='Filtered probability of recession')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(res_hamilton.smoothed_marginal_probabilities[0])\n",
    "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n",
    "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n",
    "ax.set(title='Smoothed probability of recession')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the estimated transition matrix we can calculate the expected duration of a recession versus an expansion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.07604746 10.42589382]\n"
     ]
    }
   ],
   "source": [
    "print(res_hamilton.expected_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, it is expected that a recession will last about one year (4 quarters) and an expansion about two and a half years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kim, Nelson, and Startz (1998) Three-state Variance Switching\n",
    "\n",
    "This model demonstrates estimation with regime heteroskedasticity (switching of variances) and no mean effect. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn.\n",
    "\n",
    "The model in question is:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\varepsilon_t \\\\\n",
    "\\varepsilon_t & \\sim N(0, \\sigma_{S_t}^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Since there is no autoregressive component, this model can be fit using the `MarkovRegression` class. Since there is no mean effect, we specify `trend='nc'`. There are hypothesized to be three regimes for the switching variances, so we specify `k_regimes=3` and `switching_variance=True` (by default, the variance is assumed to be the same across regimes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZuSQOPQoWyoyxpxhjCxhjv8vy9zLG2AeMsWmMsTcZY57Cd5M4UCQ1nncyn9spyvNYlrDuQ4txbG8OY93eDgDdjF5wmsxHEATRW4joRT5DZmdLBM8v3N4Tu0T0MwoSyoyxrwBwcs5PBzCGMXa4zWbfAvAw5/wiAHUALil8N4kDhZbicDgYmF0dZUMkOhwMbifLrKNsZMb6gog858FZuO2NVQDIUSYIgugzdDF68faK3bjjrdWIxJM9sFNEf6JQR3kygFeNn6cBOMu6Aef8Mc75dOPXAQAarNswxn7EGFvCGFvS2NhY4K4Q+4LGhaNsU0c5lV61z+lgWTPKfSV6IejWEta8b35GgiCIQ4GuTuYTI4WhGAllYv9SqFAuArDb+LkFwKBsGzLGTgdQwTlfaP0b53wK53wS53zSgAEDCtwVYl9IGo5yrpX5nIzB5XBk1EuWGeU+Nhs53q3JfFT1giAIordwdLE8XNy4H4VjXW/fCaIruAp8XgiA3/i5GFkEN2OsEsA/AXy1wPchDjCplO4o25aHU6IXLiezySgb0Ys+JiK7F73Q/yehTBAE0fOIJazzGTLCcQ6To0zsZwp1lJciHbeYCKDWuoExee81ALdxzilhf5CSTHE4HQ7bjLIQiU4Hg8vBkMgWvegDGWWVuJbKiJlkg+ooEwRB9B6si0tYU/SCOFAUKpTfAvAdxtjDAL4BYA1j7F7LNj8EcCKA2xljsxhj39yH/SS6yc3/XY5ZGzJi4RloKQ6nA7YZZekoMyOjnBG96JuOMuddX3Zbo+gFQRBEryGWsM7XBpOjTBwoCopecM47GGOTAVwI4AHOeR2AGss2jwN4fJ/3kOg2nHO8vWIP3l6xB7X3fyHntprhKNstOCIm8+mOsiOz6kUfKg9nJZbU5EIqueC0hDVBEESvIeoo51sBNq6Ro0wcGAquo8w5b+Wcv2qIZOIgojvup5bicDLYLjiSVCfzOVmGIBaRi77otna1lvLBEL2o74ji7Ac+wdbGUK/tA0EQhfHJ+npM/MM0cjoLxGGolHwRvwRN5iMOELQy3yEC5xy1TWEA3YtCaCkOl8wo2y844nDoJeIyHWVdbOYr23Mw0tUJfQeDUJ6+th47Wzrxr0+39No+EARRGFsbw2jvTKAlHO/tXenT5J3Ml6ToBXFgIKF8iPDIJ5sx+aFZ2NwQ7L6jLJewNv9NCGcZvdDsHeX9OZmvvTOx314rF111lMUx6U2hXF2sL2q5py3aa/tAEERhRBO6w9mZIKezEMRtxzqZ3EqCohfEAYKE8iHCX6ZvBACEYlq3hGsylTKEMsuczKdELw70giNzNzXh43X1OPGe6VhS27LPr5ePWDKFpdtbMW9zU87tDgZHWbjfu9s6e20fCIIojGhCv34jcRLKhSDKkuZzlEVGmVbmI/Y3JJQPATqiaRc2qaW6NblO45BCOZujnHUJ6/04me83r6/Eb15fBS3FsaMlss+vl494MoV/fLwJ93+wPud2qYNgZb5O4wa7u5WEMkH0NaSj3A2hPHN9A7YZUbpDlaSW6lIcRZgUXS8PRx0SYv9CQvkQoL49PSQfT6a6Gb3QHWXbBUcsjrLVqZbl4fYxesE5R2MwhqZQDEDPZMxiSQ2dCU3exKw0BmO48OFPpZubOkBCedWu9rw1ncWQbVxLZd1fgiAOTqJJEb3oert2zTOf4dyHZh2gPTKzsyWCR2du7nJt+f3F3e+txYn3TM/bgehq/I3Kw6XRUhzjfjsVzy+kJSz2BySUDwHUnnZcS+XNcqloqeyOshTKDgaX05HhHIv3zeW2Tpm9BR+s2ptzHzqiSTlsBgDBHmjo4skUYgkt66S+7c1hbGpIV5nYV0d5Q10Qo299H6t2tcvHpq2pw2WPzMXry3bneKZ5yHbFzrZ92g+CIHqWgz168cNnP8ODH21AQzDWo+/73kr9vhDOE5VIrwCbb2U+UfWChHIomkQyxfH7t1f39q4cEpBQPgRQG5CExjMWBsmFlkrBZUzmszoKavTCZZNRFtmxXD39P05djx+/uCznPggnWdAzjnIK0UQq66Q+6+NWt727TDU6Cx+tSVdTrG3Wh1bX7+3I+VzhIjsYMD9Pppog+hOvL92Fho6De5KruH67KpQP1OiVyi9fq8Ef3l0DANhrjEj2tJB3GAWS802sFre3fNELmsyXJmKMXlD5//0DCeUe5uN19Vi4tXm/vqbJUU52L6OcTHE4pKNsFcL6/yJ60RpJYMrsLbIhT8rsWGEZ5UVbm6GlOJosTkYo2jNCOZbUEEva3xzi1gof+3jzEhNMirzpNX4cYsWpPK1ZJK6h2OvChOHlmLdl/547BNFXCUYT+L/XavDm8twjMr2NcJS7GpvqaunKfeF/S3fhP/Nq9fcz9q8jR8Wh+o4ovv+fxahrL6xTsmhrM6599jOTqSJW3Msn0MVz8k7mE+XhaDIf1ZLez5BQ7mEe+HADHp/V9Xq4H67em7eBVRuQhJbKEHXfenIhxv52qu1zUykOl4PpdZQt7ZBcwtoBuJ0ObG4I4Y9T12PWxgbjfQuvCLGktgXfnLIQj3yyGc2WCR09Eb2IJTVEE6msNyWre7GvLk/YuBkEPE75mNOwVPK9diSuwed24oQR5XndZyvzNjfRUCRhSzyZwqcbG3t7Nwqms5tObW8hOuNd3U+1ve+JOQnCFFAnhVuZt7kJszY04lf/q8m6TS4Wb2vBjHUNJrfXaQjlvPc3YcjkaSfjMqN8cJ8PPUF3Jo7mozEYwx6l4tKrS3bi6/+av99evy9AQrmHCcWSXS5fs2JnG254YRl++OxneHLO1qzbqcI4rqUyJtfN29ycVcwmUxxOxmxX5ktZJvPJ90iaq13YicrNDUHb97vnvbW45j+LZb3keZub9lv0YvXu/BPjBPFkCtGk1uXoxT47yjExFJZ+HXFMsznKT87Ziidmb0U0oSHgcaKqyINwPPs+1+xsM910tjaG8K0nF+HOd9Z0e38bOqL7tbElDj7+Mn0Dvvf0YnzWA+UYDwSxbjq1vUV3oxdRZZSrUAc3F9nuBR2d2dtdt1OXCnM2NeV1du0Qn0kdwRO3lGz1pePJFFIpnq48lG/BkS5EL2JJDW8u39XjExd7mv3pqp983wyccf8n8vdVu9rxWW1rQedBX4WE8n7i0Zmb8ez82rzbBaOJLjeYQlDP29yMe99fl1W4qNGH7la9SMkFR1hGnkmdzOd2poWyYQRIgaxZrOgn5mzFBQ/Ptp149tTcbZi5oVE2ZvXBaGb0IkdD1xaJ2x6HzQ0hfPGfczG/i9GEWDKFWEJ33+0ueGucZF/rKAtHuTORfl0Rvcj20ve+vw73TV2HSDwJv9uJ8oAbgP2iLE2hGC5/dB5+8/pK+Zgos7enm/WXOec45Y8f45tTFuA3/1uJYA6nqRD+M28bvvf04v36mn2VnS2RXstUbmvUM/KNPTyJa38hBOjBL5S7J+ijShtRdwDy122R9AieKhhzOcrqvjeFur/CoPhMMeWziehFtvvaBQ9/imfm18r2OX/Vi/yT+T5Z14BfvFKDNXu6NzJ3oNjb3okPV9fl37AbJLWU6R6xv+tKi/Yq2AMRyYMFEsr7iQc/2mBy7jjnGb1WzrnhKHetwXQ5zF9PtoZWdZATWgqJLBnl1nAcE+76CEu3px2kZIrD5WRwOGwcZWUyn1PZFyGZ09kx8/NW7dYrO6zLERNoNeIW9R1RNFoa3lx1MI+/ezquemJhxuOi8bfGOLIRMxxlIDOPPHdTE9bVmfd9Xyfzidx1p9JoSaGc5wbQmUjB73GiLKCv0LejJZKRrRYuszqULibpVBd7M16zNRzH60t34Q/vrsmYGS1mv6/c1Y5XluzEK5/tzP8Bu8Ef3l2LTzc2YtqaOmxvPrRrxeYileI4+4GZOPbOjw6Ic5gPl1N01Pqmu5ZeiCeKKbO3HLQuYdpR7pqwUNv5+gKE8hvLduVse9Xaxa2RtKDKlVGOKqNY1hHAriA+kxp1EyNqdo4y53o9/R0tEWkkzFjXgH98vCnre4glrCNxLWubKu4PXb1PdIW/z9iE0be+j8ZgLGdnI6ml0B4x//1bTy7CDS8s3a+dvS/+cy6uf36p/L2hY/92hIVQzvVZDzVIKB8gbnxpGS7862zTY9FECine9QbT2oBkG6IyV73I7iiv3N2OYDSJv05PNzZaisPBjIxyjjrKLiV6IQSecF2tsQSvS8/h5lqOWrgS0UQKWxtDpr+FlAuwI5rAt55ciJ0tETQbDbSdUy0a4GgXOyHhWFI66NYow7efWoR/f2qOuuxr9KI5rO+7+h3mqhqiutydwlH2647yVx+fj2v+85lpe/EZ2pSGeHuz7igLJ1rl+ueX4v9eq8F/5tXiuQXmWpub6s3fh8d1YJqJHz2/FF96ZN4BeW1Be2cCp9w3Ay8t2nFA36cQIsq5MHtTz2eF5WTSHl5Mp649ivveX9vlZeSzIcTFjHX1+OPU9T2yUFEhxBQBB+jH+9UlO/HE7K224l4VTYW4/be8WoNL/z4n699VkdgQTAvxXMInZnKUCxHK+jF4bNZm/Hexfi2KW4qdSBTucCypmc7Ph40VaO3O2biWkuI7W/RA3JNUV727PDxtA37xygr5+19n6Pt08n0zcPafZ2Z93i9fq8HEu6eZvvOtxqjO/lx1dX2dOfa4v8v+CdMnV1TnUIOE8gEgmtAwdVUdNjeETBdFMKZfpF11lK1DUtmEcsLkKPOsVShKfHrFBbVB1Dg3ysPZRC+4UkfZkRm9kI6yxcEWwkoVytabYq3iJNbsakOZPy3m1MkYH62uw7zNzXh4+kasVGoQf/Xx+ahVVq4SDms0SxULK6p70pVZ5vs6mU90DNTvULyvXUZZHd7sNDLKFYajDCAjYmJ1xQFgR4t+fNThTsHK3dnrMW+y5Mv9bmeWLfedXJ2p/cHWxhAagjH89s1VvRIxsF6LnHNsqtePr1rdZV9u3IWSjv70rFB+8KMNeGLONny8rn6fXsd63R6sQ8HWlfmW1Lbg1/9bifumrpPRilW72jH61veNeQbpz9Xd66Mr7VSz0rao10Qu4aOK2eZCohdGu/zGst249Y1VAPSRSsA+eiHb80Sm8fP2it0Y+9uppkgZ5xxxLYUKwxTINqFPXGdtkezHtSUcxzG//1Bm9xNaCjf/dzlmG6N1//hkc9ZKK+r3VdsUNtXNf2vFHvmZBOJeabfq6qb6IPa277uA3l/tnji3RCeEHGWiYFIpjpnrG+Tv6tCWuDFG4lqGk3DcXR/hsVmbTY9Ze9pZoxeKUI11IaOsikRNE+Xhsk/mczAmh2kFj83aLBfkyHSUM4Wy1UVXl2eNJlIYO6BI/q5mNkVDEk+mTE7y0u2tWKxMQhJisCsT0FwOZto3VUhmKxeXzVGesbY+Yzgt47laCq1GA612kkQHx+7mpmYTI3ENPo/T1hmW+20jhoWjrLor0YSGS/4229RYA3qnJ6GlsKEuiI0WR9n63e8rSp/L1AHrDpF4Epf9c64pRmSHOnQtBGpPMX1tPQ6//QNsVN732fm1uPCvs7FsRytCsfR505rnHDoQCPfNei4caMR3bnW+uou1Pdxf1V22NIbw6//VFFz20ooUysb/rUqnqDWsf++zNuj3jI/W1Jk6+2LbcCyJUCyJu95Zk3Np664YBS3htHAyRS9yCJ/OfXSUYzb3LlH1ws4AEp2gWFLLMBJu/q/u5qpmi5bi4BwoN8yEbLl/8Xlbc3RMl+9oRSSu4dGZ+v34uQXb8faKPbjnvbXdMkwmPzQLlz0yF4D5/heJJ7GlMYTRt74vDaRdNkL5Jy8uw/0frO/y+2Vjb3sndrXq94LF21rwjX8vwI7m7o++iPtI2lHO32bN39yEaWv2bwa7NyChXAC1TeGsQyXtnQlsUG6Mao9QXLxaipscQM45OqJJPPDhBtNrWZ3nbEI5YckoZxN1QkR2KM6L6ihnrsyn/+90mKteJDRu2lfOzUNhXnemUA5bPsu2pjAGlqSzs2MGFCvbJmWDJF43rqVk9lmg5jpFw2ptdGNJDTM3NJge87ocpptCXEs/J5urYtdAhmJJXPvcEnzrqczMtEpLJC7devU7jEtHOfM5qsBrjyQQcDtRlkMoq59BIBwX9TwB84E9AAAgAElEQVTa1hS2FSitkTjeXL4bF/9tNl5ebI4phKLJbjuea/d04KcvLbN9XqkyeqCOJFiJJjT5PbWG4/j1/2rkNbS+LohVu9tx6+urcu6Heo6oQ8517VH8+IWlMit/IJixVndMl9S2yscWbdOF/e7WTpMDmsvhOlAIR7mnyweKkbUleTo5duxojuC2N1bK8o4q+2um/+/fXo1Xl+wyfW92NIVieHZ+bd5sdNQSvVDb3xU727C1MWQyBFRRKc6LE+6ejmPv/AjPzK/F9LXZhUdXSqOp14FooweX+nJnlBMpBDxOeF2OgvK9dp0xRw6hLNpGO0c5/ZqZpoOIp2U7p8XxVK+3cCyJJ+dsle+jfhcAZHtY3xHNEOddYVdrBMf8/iP5eySu4S2LI727LVO41nVEbecu/G3GRqyv6/pkxHvfX4ez/jwTTaEYvvHvBVi8rQWfFhD1EuevaIO7Mtpx9ZOL8KPnl+5zzKq3IaHcRaIJDc8vqIWW4pj80Cycef8nuOivn2LZjlaT89AcjptugHvboojEk3hm3jbTkFVEadCyDf1nZJTj9tuZJvMlM8vDCdKzVdMneDLF4XQ4wGwcZZGhdTDzxEK7BU3Ux2RG2dIYqUTiGo4cXCJ/HzOgCGOqizBhWBk41/ObLeG4nJAm3E4V1XVVh+pUfvrS8ow8r8flMAli9TnZXBW7zoeYPLJ6d+5GqymoxChMjrL+/LiNC6SuNtYcjiPgcaJEWazEiuooB6MJ2fkCzMc+2yz6plBMvuf1nxuDq04ZIf92z3vrcPzd03HTy8uxclf+JbTDsSQ+/485eG/lXttjU+pLi2NVNDeFYibh+vD0jfjmv/VOyNPztuHVJbvw4sLtxmdMyudYiSY0fLi6DrM3NqJOmcjSrGz7weq9+GB1Xbcdm+cX1Gach9kQHUZ1lEJ8504HM7le+Toi79bs2a85Rn0f9P/VjlRHNIFn59fqgq2LMabuIoaZl9S2dntVvb/O2IiXF+/EtDX1Gfu3v6IXfrd+nbVkEYR3v7sWb6/YjZ++tAx3vrMGmxtCttsBegdbiITF21rw38U7TIL0t2+uwnl/+VTG2cSKoQBQEXCjLZKQsQJBLqGab/7L1sYQ3qnZk34t45oYUenHzA2NWLzNvvMSTWjwu52oLvZmVCnqCtlig4D9vJJ0rjv751G/b3F8Kop0RzmbUG7vFNGL9DGcsa4e976/DqsNI0bcP8X3VtceRXWxBx3RJF5ftks+L9vCWNaOk7VKSGdCw6Kt5uNsjV4ktBSC0WTGORhNaPjbjE344j/m2r63lWLlnvHYzPT6DaLiTXcQ7VU4z2S+eDKFRz7ZZGrf+nK9doCEcgb3f7Ae82yWCX505mbc8fYavG8sRQwAG+tDuPe9taZGoDUSRzCakA3f3o4opq+tx13vrsU1z6QFmzqRx27YHDBXSAC6Fr2Ia6mMcm3yPY3XUx1oLcXhdMA2oxzTUvC6HGCWyXx2Qlx9TGzb1pm+yO0arkGlPpQauemBJT588svJuNIQaKFoEifeMx0PfqQ7102hGHa3deLYYaXy+XaOsvUYTV+bmYP0upymi1ztqGTrJdvliK3i+W8zNsrJJipCzDmYWZSIxl0V6pxzrNzVliFofR6nLKdkR0y5kdZ3xExOjPqe2UrFNQZjCMaS8LgcuO3zR+OYIenjLPbznZo9eGHh9oznfri6ztQoqm64eg4I1CiH+okm3TsDJ9wzXf6+qzWCXcYELZ+RkxYiQdysxVDq8h2tWLOnHRvrgzjxnum44YWluPbZJajviGJomQ8OZhY+YoXEj9ebRxtykdRSuOPtNbjk77Pzb4x0BEltH+LGdRKKJuWNtsTryjkUHE+m8LOXl+PLj+oTHx+duRl3WiqVFIK4ZtXz49XPduLOd9bgC/+Yg+88uf9L+G1pDGFbUxinjakE58BD0zbYbhdNZMbTAGBImQ8AsLE+mOko76eFJkTEaWdrpssXTWh4et423PzfFVhoiJ3tOYaxrSbIH6eusxW6ouMeiWuyDRtc5kdrJI5GS2cw2yhIfUdUjlhkY8a6emxtDGN4hR+APtHL73bKSkPf+PcC2+dFEyn43E5UF3vQlOX9Oed45bMdtm2otV1OKaOq9tGL/LWn1e9bdEBlRjnL86SjrOxji6yEoR9n0ZbFtZSMvFx4zCAAwPsr0/f/jmgCLy7KbA/rO2J4XmknrWI/FEtmjKZYoxdiP61CWRgt2UaNrddMRVHaiHh63ja4HAyHVRdha1P2zl221wvH9JFecWyzjb6+v2oPHpq2EX+fsVGORKvzEbY3h3N2Lg9GSCgrxJMp/Hv2FlOvUSBmVFvFa1xLmVzC5pDuKB9WXQSXg2FvW6dt3cmIIiyy5cqyVb2wNjpC+HpdjpzRC+uNhHNuCGVHRkZ5SW0LOuOaHIZyOdOnit3EMfU9hUAzD29lfsbKIg8Gluo3vupi3QkQQ/FW4SCcyTPHVcvH9qpC2aZWaTYHzmONXiRTaA7F8OjMzdmFsk3nQB16W7e3A3+bscm2fJFogEdUBmyjF+r3vGBLM770yDy8sNAcfwi4M93kaJbO1sfr6vHcglr5uzoknU0oN4ViCEWT0rUuVyYOArqYc7DMG/+u1ghueGEpfvxCuhxRvkiByf3OMewfjCYRMmI4osGeMnsrfvTcEqxVyl91RBO44rH5+MI/5mJLQwiRuAaP04G4lsKetk4MKfejIqDf4Lc3h7GnrVN23JpCsS5nLluMc7Krc9/ENdEcioNzjp+9nJ4Q9OcP1+PHLy4DAAyvDGDh1hb84d01tuJQdDYagzGkUhwPfrQBzyqVSgqdVBOVYkQ/FjtbInKS6KaGEBbXtuBfn27Bgi3NWLAflk6PJjSc/5dP0RFN4syx1bho/CDM39KM+VuaTNddMJrAUXd8iMdsVjAtNjrWulA2tylq5hvQBeVqS1yrK4h2cHtzBB3RhDJapdkeh21NYfzs5eV4bUlmGUXrPnZEk3h/5V5TlA1Id9CbQrG0UC71oi2SwGbLnIFsTvdFf52NX/9vpe3fBEJ4XnPmYQD00mHlATeOGJSOvtnVlY8mNXjdjpyOcm1zBL95fZVJTMrnW/Pk8aSMmOSKXuSqMa5+32mhnNtRFgJZzWZLoRwS80iSch9ExYjxQ8vkZxTMWFeP29/M7LDe9c4a3PFW+nHr/b+9M2GKOQ4u9WFDfRAJLYUps7cgGE3I+19LJG66z+TLoFvvzZWWdvyIQSUYP7TUlHPf2RLB6Fvft53voZpqoVjSdC/J1u6IcnRLtrfKfVfv1Xe/uxa3vp77PD3YIKGsUN8RBecwVVMQCKFX125uJGIJs1BujcQRiiVR5ndjUKkPde1R2+FFtaesCge1kbL2pjsTGna2RHDUHR/ilc92ZDwn4HEinuRZoxdqz5ZzLm/kHqfIKOu/L97Wgq/9awGeW7BdxijyO8rKZzAcbbVBFxeYen8YUeHHAKPGr6j1O7wiAMB+cgMAnDk2LZTrbaIXaqNbl2XGsNcSvdjcEMTPX1mBBz/aIIWMFXtHOf2Z1RtUxtCbEb0YURGwuIuiCH/6sbnGaEZ7ZwIjKwPycb8n81JtiySwalc7/rt4h6mB/NMH6/EnI1LgdTlM5+eetigqAm5cPH6Q6bV+8UoNPl7XIIWIdeLg2IHFOHpIacZw4542/TuYsyk9CqMK5fbOBBqCUVPsQR0yzzZ8CegNM+e6mG4JpxvlaWvr8dTcbfL3NUq8Qzhq3z5tFABgQ30Qg0t9qCzyoCUUx89fWYE731ljupEu2547iypQz+dcudTv/2cxbnxpmTwOjUF9NORddchbeS3h7v1nXi1awrqofnvFbikuWpXPXqNEXyLxJF5atAPH3TWtoMk5wpF9c9lu/N+rNZj80Cx8YnHY7/9gPa56YiGuemJh1mH5fDQEo5i/ucl0/CqLPRhTXYRdrZ24+olF+OVr6aWRxVyE15dmGhZimH59XTCj02atv/7ozM24asrCLtVXfnvFblm2TEQjapvCOO6uabjBqEl759tr5Kjg8SPK5XO3NoXwbs0e/MoiUiPxpGmEBNA7nDtaIqb5GUBawDUGY3JRosFlfrRF4qbJoEB2oWzXyV+6vcXkenYmdPNDVLJpDEZR5nfjvism4FcXH6l/biOH+9s3V2H87z8EoB93n0uPXmQrNyY6nOpkQYHV/e+IJtPzSmwihTJ6kWWUgDFz2yGEtTqZj3NuqtPOOVeqXqSPoTie4n9xHsWTKXnvHlUVMMUYgOxu9y5L3lhUnfjDl8YDQMbk71PHVCIYTeKhjzbgj1PXY8rsrXJfODfvq3ocxWdOaimMvvV9TJm9JcOQElGULxw3BNefMwa/vPgIjBlQjJ1KLf4FW/XO34s2JTRVYR6OaaaOS7ZMu5jkv3xHuq2q74jizeW7kNBSaOtMoCUSzzpqdDBCQtlgxtp6uarZ9uZIRg9YiExro7WpIYTJD82Sv9/2xiqs2NGGEp8b1SVeNIZitkXjf/jsZ7J+sHoyqjdQ6z7EEprsmb26JH0TEYI34HHpS1grPVB1Epp6EYViSdkLdzlFRln/mzphQQwfqw6IXXZRfU+7Id1wLAktxU096YvGD8bAUv2GMcC4cYwwRINdTdSKgBsTh6dvUC3heEYhe/WYZct0e1wO003ljrfXSKGX1VE2dnxDXRDffnIRZm9sNPX01YmGHRbx1xSKweNyYGCJ11z1wuIoX//8EpOLdtExaTFb7tcbvHu/fCxOOawSgN4pmzJnK+54e3XW+tGDy3zY2x7FbW+sQlJLYXdbJw4fWIK7jEZbpa4jiiKPfjOosDgRAY8TRV5XhsOjTlbdYpzPagZer2P8MU7/U3oJ1GgihR+ceRh+ccER6ExoWZdCFTdC1WFREe73/C1pkf7WCn2SzKgqvZPRFklgUKkPVcUeNIdjqG+PYm97p7wZup0MS3eYhfLyHa14f+Ve7GnrxJVTFkhXUhUouXKiszY04v2Ve6VweKdmD255tSbr9iMq0h2ina2dWL6zDTf/dwXeWKZ/FvWzT1WiX3vaonIEo5AawuJaCcb07KU4n62VSG679CgAwKuKY9oQjOKBD9d3aRnbKx6dj6ufXCSP36BSLy4ePxgjlI7gTmX/RXWbQcZok2mfxSIjrZ2ZjnI0ie3NYVz+6DzM3tiI7S0RBGNJ2SleX9eBn7y41PQ9tkcSePWznXhyzjbc/+F6aCku2wAhIGZuaERrOC7PLQB47YbTUfP7i3DSqAqTIFBRR2/uu+JYLLjtPIw0zks1pw+ko0QNQdVR9iEc10yTw4HsQtmOrz6+wOR6RuN61liMFNYbjnKx14XJRw4AAKzbq7/fS4t2IBzX6xhHkxr8HieGVfhNrreKcGTVTq0gM0+eUCbsZXeUhcHyq4uPxMf/d478e7HHZeoYZUQvYkm8tnQXznlwlizzFolr0iFts3GUxf+iEx1THOVBpT456lkeyD1h0Fp5SbQD1pVVf37B4fjpuePwk8njAAAvGR01t9NhK+Stry3KfwrH+p8fb87YJxExO3JQCW679Gicd9QgjK4KIMXTuWhxj7ebK6V+N+FY0vT6HdEkogkN97y31rS/Vo10xKBirK8L4hev1GDG2npE4hoagzEcdceH+OuM7AvIHEwULJQZY08xxhYwxn63L9v0JsFoAv9dvANbGkO49rklctixORzHUXd8iA11Qczf3ISvPDZP/s3aaNm+biyJEp8LxV4nwrEk6jtiOGFkuWmbplBczthXHeXvPLVIivLOuIYyvxvfmDRc/92opwuYe5mikfB7nEgkzRlldZU+9SRvCcdlo+F26jlk0btTLw5xEalLWNs1EKpQTtg4zuG4ljHzdVCpDwNLvGBMj2EA+v9FHqfpxim4/PhhKAu4cc+Xj8XPLzgcQDpeka56oSzUkSXT7c2xgEY2B0OIiJkbGjB3cxO++/RiOQwnctZXnDAMQOZqWo2hGAYUe+H3OM3RC0tG+aM1eo7ryEElGDewGOcfnRbKQ8p10fDt00bJz94WSWBTfRAJjcvOjVpmDwAGlejPe3nxDqza3Y7drZ0YWu4z1UYeU51+jnCUhRMhCHhcKLERympOXKwGpsYphACIaym8sHA7Wo3Ojc/tkO8VjtuLZXWpVFUsXnPmaABAeZEbh1UXmcSjuAGqbvzISj+qirxoDsd1NyMURziWRHnAjfFDyzIc5Ssem48bX1qGn760DAu3tshZ7+oN66w/f2Ib2VDP8Vkb0qMTudzYSiVH+OLC7Xhufi0AYJVR61q91mdvTHcKdrZGZJa92cbF294cxnefXozb31yVIUaaQ7GM6/ixb52Ip743CY9+60RcNnEo3v3pWZj9q3Nx/TljceXJIzB11V7c9PJyPD13G259fRUem7UFy3a0Yf7mJmyoC5o6jlqK45r/LMY9762V16gQjo9efSKqi72m72hwmQ+dcQ3bmsJSeNoNM4vPkUzxjKHfUCyBHzzzGWp2tuHjdfXy3BTH6N2aPZi6qg6n/+ljPDFbX1Do568sx69fX4lVu9vRFklg5a422+zljHX1JiHhdjpQFtDPv2xl7lTntTLgwZAyv8xYl/rN7qTo6DSHY4jE9bkC4rywLgBUSNUJNfMrqlfo+xiVnfDDB5bA5WAZFRUaglEjo+zAiErdyLCLtYlz0G5iaoaj3JnMWqnIur8AUORxYnSV3k753aLTrn//CS2FZ+frrnmZ3w3G9HtUjdHhErWM29QKH9GEbHPSGWVDKCt1gkVbPrDEK0c9xxoVmrJ1WLZYJsqJNlCYD0IoDyr14ZcXH4nDBxaj1OcyjcSpnQ2TeaZcE9ua9HNGnN9etyOj8ov4jINK0yMYA417gnC6halrN1dKfSwcT2aMFs5Yp4/u/WmqPoKZSnFsbgiZTJ5jh5XJn7c0hhBRXudxS0ncg5WChDJj7CsAnJzz0wGMYYwdXsg2vU04puHWN1ZlzEAV1Oxswz3vr8MyxTHIFUL/749Ok4Ky1OdCkceFcExDfTAqG0gV0bCoJ//G+pBchz4S1zCkzIc/XjEBgO6QClGsOp9JjcPBAJ9bzyirQlWNSagTHILRtKOsRy/SjrJ6U/VIRzl9qtgtMW0XvVCJxJKy8fvqicMx59fnAgC+e/po/P3KE+A2MtCMMYyoDJhcbcaAz08YjFsuOgIA8J3TRuGiYwYDgHT7RHxBdVazTX4UcRI77CafAXpjfNPLy/HeSn343ON04J+Gm/fzC47Ary4+Et+YpE9EFDfoN5fvwk9fWoamUBzVxR743U7bqhedCU0em+piL575wcmYccs5GKycM+r5IxrcxlBMurii9vEEpVECIB17AFi4tUV3lAeVyMlxAHDzBYdjsOHeCZd2aJkP93z5WCmohaNsFVd726MyTiMiS6IRHFzqM00u+t1bq/GLV1cgmeLwudNVPELGhBnBi4u24/JH5srRk47OBFrDcZw8ugJv/OQMXDxe/+4bjA6o9cYEpOMMADC6ughVxR6jAo2G5rAulIs8LowfWorNDSGkUhxPzd2G7z2dnsAmrnvhSIkbI2P6jV9d0bCuPYqbXl5uOm+7inpTfG3pLrkwgRilUPOUG+qD0plSY0LiptcRTeDvMzahJRzH/R+sx6KtzXhx0Q48PS8dVUlqKZx07wzUKIshXHf2Yfj8hCE4/+hBuHj8YPzzqhMwYXiZdEC/Pmk4InEN79Tswd3vrZWL0rRG4rj6yUW4+G+zMfa3U7HccOfrOqKYuaHRFJERYlAMj4vXBgCfy4kLHv4U5z40C2uN9q+uPYq2iDlnrF4/1uznpxsb5bnQFIrL0Q4hdsT5FDPmonDOZdRJMHujnpc+S5kL4XE6ZAfspWtPxVs3nin/NkbpmFpzx+pCD0IMimu6xOIoC+HJObCnPQqfyyGP0+bGkEnoiLb77RW7M8qMZUOcu50Js6Oc4ul5IR6XnkG2LlCxp013730up4zG2RkZLcJRthXK5ra4LRJPT+azq3phCDS5OqxRovQvX5+I9286C8W+dKf9N6+vlJPnvG4Higy3WZhKwWgSt7yyQuZiJwzXKyuJ2Fg2RzkYTWJPWxQelwNlfrcc9RxnCGW7uUd2iA61aLfFueQx7nkOB8NXThyuHBvzCJr6fajHUQhkcX57Xc6M6IW4/6tlOKtLPKb9D0oH3fzcdXs7cMVj6ZVTdUdZ32ZYuR917VH53a3d24FgNIG2zgQicQ2nj62SzxP5bkBfidBuLYGDnUId5ckAXjV+ngbgrAK36VXEDaetM266sQpqm8O2sYlsBDxO2Vsr8enDWaFYEg0dMQwsSQ/dCFojCbxTswcPfGguUWVq1DxOuJwOuJ0M0aRmu1RxIpUytnEYVS/MdZUFaka5M6GZohcOxVFWIwteQyhlc5TPPly/oUxfWy+fbz35nQ6GlnBcOggnjiqXw64jKgP40sShpu2HVwRMHZKhZX489q2TTMOVRwwqhs/tkMO0MnqhXOzZHOVcSzJna/wagzG8U7MHq3d34IhBxTh1TKV876Hlftx47jgMK9fPIdGA/eKVGry3ci8agzFUGY5yRMllqUOPIrd28wWHY0iZ/jpFnrSYHVyWPj/Febt8R6s81mK46xxj+FQ+Txm+/o8hlk4fW2VUM9Ef97nTi5kIl5cxhu+cNgpDDSc74HGabk6CuvYoxgwoxqBSr3Q4RPRiWIU/w3kSrrPqKIeiZqfi9jdXm0RcMJpESySO4RUBnDiyAscM1StypDjHqUYMReyjeG1xHQLAYdVFqCzyyPMhlkyhMRRDsdeFoeV+tEYSeGzWZtzz3tqMMkYjKv3YWB/C7rZOObS88d5Lcf5RA/HSou2yg3j/B+vwTs0ePGu4wVZ+PHmsHBmyMml0he3jG+r0CWvW2MmEYWVwOphpyL8xGEMwmsB1zy7BX2dsxL8+3YJtTWGcNa4aYwcUYdn29LZ2ZdSGlGW2fyonjqwwicKdLWaXWN1nu8eBdHUIMXo0SPmOPlnfIM8V8X9DMIYHP9qArz4+X96Qo4qr22xx9Os7Ygh4nJg0qgJbGkPyWr79rVWYvrYe25rCOH1MFe674lg0heJYuLUlo636dGMDOqIJHKWUroxrKXlNnzqmypRPVkdjxMqnggalNOFoYztxnD3OzDZIxAbq26PwuZ0mYXXk4FLTtq3hOG7+7wr8/JUVWev5qvlPce52xvV7ijqqps5HKDdK0qnsMmIuPrdTxoTUOSRLalvw6pKd0vm0Lp6TtJlgbl151Ip1UppYxe+rJw3HmAHFxr1VH4lSOwtupwNFxkiuEGS72yL4ZEODjNeJNmNrUwh3v7tWZmqlo6yIzQ31HRhQ7AVjTDrK4jqwy2Lb0ZgleuFWvoNbLjpCnnPthjEg+NnLy7HE6KyrQlnkp8X/HpdD3pvv+OIxmP2rc6UB5VWMEfE5mkIxNIdiaDSeH5Mjm3VYtasdi7e1mL6nkJJRPnpIKfa2d2KncR6s2t2Ocx6cJY9JRcCDv195PC6bOFTeFwFgS1O4S4uCHWwUKpSLAIizswXAoEK2YYz9iDG2hDG2pLGx5+vs+dx6g9EWScjeIgDc/vmjUeZ3Y93eDrSE47jqlJG2DZsVv9spy7GUeF0o8rrQGIwhFEtiUKle/uyDm8+W27eE47jp5eX4zChs/69vnwggXf6nM64pN3/djRQNuzUT7HYwXSgnU1ljEGoD0BnXZG/TbQhl8bRIIn0jtcsoi4vlL1+fiAe+dhwmjijHve+vw1Nzt+G655aYViZ0OxlGGIJJXIi5HF1AFydqQ2zXkLqcDkwYViaH19ITQ7riKOcSyvaNnzrMO6TMD6/LIY+z6EQI97beUiS+timsO8oeJzhP76soFRZLpOTNpUK5aQWUySPqRBJxA1WH84Vb96WJwzD1pvQ5puY8G4IxFHmcmDCsDIwx+Izvwa/clK0TVsR35fc4ZcdPZW+HPloyuqpIuqnBaBIBj1MKIhXxOX1up3yvUCyRswZuMJZAazghbzSlPjd+ccERePm603DeUelmRQyJBjwu09D2sHK/qcMA6Df6Iq9TNuIPTduIicPNbjwAXH3KKDiYvqJeaySOMr8bbqcDl58wDE2hONbs6cDXHp8vXWBx/owbqO/Ld04bhZo7L8JvLjkKD3xtIp655mTTdwwAn58wBDW/v8j02Bljq5DQOC5/ZB4aOmLwuhxyVGFImQ+DS32myh+NwRhufGk5lhgxkreW78bOlgiGlvtx7LAyzFhXj+8+vRjhWNL2WIsOUTYY0928h74+0fS4GNEQnd3fvrkKo299X64EprK9JQLG0u6Ww8Gk6LQKo6MGl0BLcby3ci9iyRSWGp8r31LKZ4ytxhGDS0xxiJ0tnXhuQS22NYUxZkARThypd0yuemKhKY991rhqLNvRhogReVv02/Nx++ePBqDPRfG7nRmu8WHV6WoR1munIRiF1+XA2rsvlu8pzkO7xVFGGtGC+qAulIco38lhVQG4nUx2ntXh+F+8sgLtkQQsu2Zbe9nqKAMwLWRU5nfLiIIQ/nvaRPTCiYElXridDDtaIlKIPzlnG+55d21aKFtr/9pkX9V21q6dtsYArLn5Yq8Loag+KUzV4G6n4SjHk/I9Vu5qN4n/Uw/T3c6/TNtoGmlpCcdww/NLTctTr9zZLiNCQmAOLvOhyOO0jV4MNa7Rr580XF7T4jwtC+ixECGUPYr5VOpz48Offw5HDylFe2ccLZG4aRRBxLjUCEu9dJTV8qP6eXX6mCqMrArgD5ePx/fPGG0aIakIeOBg+ndw0r0z8I9P9PiDcJavf34pLntkbkYHPRxLyvvg0UNKkOLmidAt4bhcpKcs4Mblxw/DP686wTSqudWIXqjkq/19MFCoUA4BEN2E4iyvk3cbzvkUzvkkzvmkAQMGWP/cI1QEPGiLxOWFef5RA3Hd58bgtDGVsk7mccPLsPE+3UUC0tcT65sAACAASURBVHkfn9v8kfwepyzjVeJzodjnko3VwBIvSn1ukytjRbgNYuhKNGqALmaiigusktR0R9njNMrDKdvkcpTFvrmdzLTgiDqbVYhKl41Q9rgcGFLmx5s/PgMnj67A03O3YfraelMNYJ/LKZ1FsXpcLqEKpCeuCdSLXOXYYWVSLMgSTklzZ8COXI5ythXS1MeHlvtMC7CIm6fP7URVkQc7WiKmnF9nQkN1sVd+l+LGIBYaiWspGcNRJ9GpOWIVn9sJn9sh3TshoMTwpNrps2aNLxo/WLoMfqUTJkRtscUVE4tmBDxOFHlciCbS51dSS2FXSwSDSn04rLpIRi9CUT2jb7fqnnDRfS6nfK+3lu/B5/8xx/azAvqNJhRLmkod3XzB4Zg0utL0WauMERu/21xz2uV0YJhlxGhHSwRFhqMs+N4ZozPee+KIMnzxuKF4ceF27GyJoMo4TsKVenP5bilOgXQ067Qx+t+tx2HykQNtHcCygFvOY9jyx8/jpetOw31XHIsN9UG8umQnKgIe+T0PKvVhaLlPHsuxA4rQEIxh+fZWXH3KSDxy9QloCMYQjmsYVuHHscbQ5+yNjVi3t8O2rFM+RxkAThhZga+dNBz//s5JOHNcFVwOJss2njG2CiVelxQtohM3VIkM7WyJoNzvNonNt248E18+3jyiBKSrSghRsdCYWKeKKrtO7fEjymxHB+dsakJbJIHDqotwxKC0WzztF5/DyYajf/WpI+XjZQG9atGJo/S/ba4PosibeT2OqgrIkRlrmfOGYAwDS70IeNLXlIheROIaXrvhdFx1Svo9RxmCrL4jBp/bYXLiqou9+PZpo3D9OWMBAK8t2SWjS+/U7ME7K/eY4lQAEI1nuu8R6Sint1XPz4qAR45uCUN6d1tEzitwOBjK/B5Mmb1VTjzeYUya3GbU5rUKLDshrMYJGoOZkwOtMQAHsxHKsaRpMSdAbwMHlnqxqyUi3VC10+R0MBw9pAQelyNjpde9bVF8aCy3LGMbsaQcDRCRhQElXpT63bYdNXG+VBZ7ZPsmzlOfywm/2ykXPXHbmG/lfjf2tEUxZ1MTjhhUgsW/PR+HDyyW+yruaaU+lxTIQjAHo0kZixSdtkGlPtz1pfGm93I6GCqLvBnxmXV7O3CjUbISyLwXhqJJ7GrtBGPAyaP19m3xthYcO6wUL157KgDIqjnlyjklKluJfbQ2f7VN3Z+I3NMUKpSXIh2lmAigtsBteh0x1NSZ0HDZxKF46vsnA9AdIeFkilI+PuPiEbV8zxhbjQ33XiJfy+92ym2KjeiFQAiRXM50ecANv9sps16dcU02fj5DKKsugbjhJlIcbieDx+VAQuO2FSgAc0ZZFd1uGb3Q/6aWo5JCWdlvMbwj/uYwipjblQ3yunXXTp+lnjI9LxsBJXJw03nj8MDXjrPdrrrYi2hCX0FMdHTU2Ijdsqn6++d2tK0wS/3gyiKPadEMVTSfNrYKry3dhUv+ZhZ+1cVeVBkNhqhhqbr9ItesDoNa3SuVioAHyRSHx+mQ7qU4rupriBjENybpufCHv5F2BNVOmBAB1tX/nMYNKuBxpSffGY3x8wu3ozkcxwVHD8Jh1UVoDsfRGo4jGEugxOeWHa/PHZHZCfa6HfK9nrdZxERFONXlNg41ALzxkzPw9yuPlzO81fNHCFtVEAP6taNHL9JCTl0pUlBZ5MF3Tx+FcFzDzA2N6dhAqQ+jqwJ4dkGtafstjWEUe13SabQTpQ7le1X39eXrTkPNnRfJ7/3Kk0diWLkfkbimtw3GtgNLvFJEeZwOjBlQjM0NIQRjSYyqCmDSqHQcZVi53/S5mkJx27JOQ/I4yioXjx+MF689DaeNqcKaPfoNvKLIg2ql0/LJ+gZUFXlQpnRutjeHMzpuQFqoqfGuyUqEyO92YrEy9CycTrtJbROGl5uqiFgZN7AYTgfDS9eeik/+7xyMGVCMMdXF8DgdclEJIF2VQpwfe9qj8vxS8bnToxI7Wzpx0j3T5TC5iNzZfdZwLImTR1filguPkH871ehcxZMpozOsnMfFXtx52XjcdP7huPrUkXh63jYEY0l57YeiyYx2VRWsQtSJFfbUbauK0t9becCNVqN2rzBEdEc5fS/62Xl6lYZ3a/aAcy4Fl+g0qfNfxHtaEeLxsolD0RyO49GZ5kld1goM1rZQny+hydcRBlRnXMPxIyqwdm9Hxmp3gC7aXMbIKwC5AumY6iLTfVPEm8TfAOC4YeWoLvbi8IElKPa6pAN7wzlj5fuLTlgskYLTwVDsdSGhcTCmn98BjzPtKNvcB8sDbqzd24HGYAw3n384Bpb6cMLIcqza3Q7OuTSCRlcXpR3loJhEmZD35oBNp06luthjuziNuqCauLYBvZ2q2dWGHc1hDC3zy88b11IYUubHGWOrUFnkwcwNhlBWrnvhKIuYphV1ZOxgpVCh/BaA7zDGHgbwDQBrGGP35tnm/cJ388BR5teFciSeREBpmNQAuhi+FmJG1PIt97tNokt3lPXfvS6HKWMqbhCMMTz9/UmYd+t5GY6016U7e6qjLG6kfrfTlCsG0lnmpJaCy6HnmOOWJaznKaWz1GxxNGGNXqQdZXVCm/h8akMlhbJyvIq8LtuFTppCMQwrD6AhGJNDvrkcXSDtdALAkYNLM5wS+Z7GdiGlJqdakzhfRrkrcRrA3DvW3yOV0UMXfMWofGGlusSLc44YAI/TIZeQVSsk7JVCOVNIDLWZCCpuuJVFHtNkHMDsVIgZx5dNHIoRlQGT0yrcYp/bIZ+jul9Aun603+1EsdH4hoyRifdW7sVxw8tw8fhB0gFcur0VQcNRFg7zhUcPzNh/n9tpWr46F+IGPMLGKQT0/Ozlxw9DsccslFfddRHm/EafNDqsPPO5RV6XKZoiRIdKZZEHJ42qkMdYHRE6c1y17eIjQ8p80um2q7X6wg9PxQ3njMWC287D3N+cJx/3uZ0md8/pYPjhWfrCEOvrgvI7qir2SuFfVezBwBKvHMUZXhEwDdkOq/Dj9LFV+N7pel3pxmDUVrxXK2Kpqwwr98vOXmWRxzQHo74jhmEVflMbl+KZCyAA6WXMjxlSKuMDJ46qwGs3nI5rzzoM5x01ULa9YnQmG8cNK5MZ9kuPHZzxvUuTY1w1xhhRnRsmj8U/rjoebqcD3zWOkzzWynGxXhsC4a4Bunj/8YvLwDlHXUc0o17yEYNKcO6RA/Dnrx5nfPb0a557ZPo6EbEocfzUY3uykmm/ePwgMKYvhGUdqVBH9prCaUc5YMkoDyhJv3ZZQI9eqBGruvYoosmU3JfvnTEav7nkKKyvC2JjfchU5UZ8f61Zav8KxL3ggqMHYtKoiowJ9fmEconPhWA0IYXyI1ediN9/8RicNa4aJ4wsR0LTj7+1ky6uDdGBvvOy8Zh609l48bpTM95vtDHZVDjKE4aXYcnvLsCAEq9sOwHg6lNGosjjgsflwHjj3BNmhejUiRVu/YpQtnWUjeeNqPRjknFeTRhejpZwHDtaIvJYjqwMSFdeRP3iWkoeD2sMyMqAEq9pERA7RCQU0CtOra8LYtbGRoyqCmBImV+OMg8t84ExhonDy2R7oLZjXpcTtfd/ATcYoyEqPrcDy3Z0rY59b1KQUOacd0CfrLcQwLmc8xrO+e/ybNP9JZJ6gIqAB22dcTkkJVDLuUlH2bg4Jo2ugMfpyBA1PpdTvkZnQjM5EGou8byjBmFYuR+jKs0xDJ/bgYoidzqjrEQvfB4nOhMpk1BuCsXQFomjvTMBl1PPKCcsS1jf9sYq+bO6GmBn3By9UBccUYdc0uIr3VAFLY4ykHlhqis9CVdGOIP5HF3VZcvlPhcbrs/Li3fIWrqqOM6XUbZOrsxGleXG/KXjh5qiKKq7/LkjBuDy44fKOr6CakPQnnfUQFnOTBXKYnjQml/99FeT8cHNn8vYJxHRUIWy3bE6eXQlVv/hYpx9eKar61dGK0SjnbIoP1GHO+Bxotirv4+obxyOJTFENJIjyuFxOvBZbQuC0SSKvS7c/oWjcc4RA3CRUaVCdav15XC9XeqsiEmTIoOcDXG9iWuwxOeW4saus1XsdZluVl6X07R0N6AfZ8YY/njFBFxz5mj8/rJ0/emvnmQ/OW9kZQAXHTMIV50yAr+86MiMvx87rAy3XnoUhpT5bXPcKmLhlC9MGCJFm8vBZJSkWhHNgF7tQ+0MDS/3w+104PeXjYeD6XEAtfzZzy84HBvuvcTkcncVUSoM0I9TlUVsD6/wZ0zUzeUol/jcqC72wuVgqC7y4uTRlfjdF4/B4DKfFADRRMo0lCsYN7AY158zBhVFHowdUIy1d1+Mx799Eqb94nNYfPv5qAi4cddlx9iKk8Oqi3DJsUMAALd/4Wjc8+VjccExumj1uByyPVKND5W/fH0ifnruOPl7YzCG299ajW1NYUwcYS4L6nE58J9rTpGPq22h2mkTHS1xjaptkCpCir1uBNxOhONahiBVJ6LLUUpjgrgnm6Ps9yCeTGHiH6YB0IXv7rZOaCkuxTsAfO4IvcPx/MJa03sKg0kdlbS2w4ylR7q8LgcGl/nQEDSLtnxCWUYvQmLVUz9+cNZhcDiY6d6tTvYF0sf4zZ+cibdvPBM+txPHDC3FkDK/adumUAxHGRMoD6vOjEuq7ZbbpQvggMeJ844aiMe/dSJ+PFkXhWmhbFQPcrvk/dXuXCwzYofjh6SNujOMChKzNzbKYzmqKoDmcByxpIadrRF5bm5pDMHlYHlHba2dTWtsyIoofdoWSWBUVQBOB5MjVaIjMaoqfZxKfZlC3RrF87udOOWwqi4v+NSbFFxHmXPeyjl/lXNety/b9DYyeqFMnAPMmT3RSD309Yn481cnYFRVEf5+5fH43hmjTK/lcDB83bh5njSqwiQe7ZxCq5jSHWUvWowLKRLXZJTD53Lo0YukOXN8/N3T8dGaeridDnhcjowFR1TU6EVnIiUXvBB1lMXT2m0yymp5OGv0AkDGsKTP7cSnv5qMqTedLW/qYoEVrzv3aad+D9ncZCAtzh+atlHuezLFZWcin1C2DscLrI1ylXJzX/K7C3Dc8HJTFEXd3u104O9XnoAZt5yD5394inxcDEsfP7Ic9R0xY9GLpOxQLNvealoxSzCqqsg02UYgJo1WFnmkI5fNqc/mLsjohccpO0LWKgDiuPo96XiGcJt0dyotRCeOKMPCbS0IRhMo9blx0qhKPPuDU/ThTgeT+T1AP5+dDmabJ7XD63LYusLmzylK2eV2U8TnFp/n8uOH4vtGPvmZa06WE9ZKfGkh/YXjhuDOy8abjuUJI8ptj/mIygB8bif+9JXjsp5jXcVjTAb725XH43dfOBo/mTwW5x41UL5udbHHVIpJVJP5iXGjFjdEp0Oftd/QETM5yg7Guh1FEqiVGCqLPBk32+vOHoPvnzEai28/Xz42oCRT5Irz1+d2YkiZD4NKfSbhXl2sL9QTiesLHFSXZLalV5wwDLdderT8XZwDRV4XBpb4sOyOC/F9Y9nmXHhdTnzntFGmYyJGlOyiF4De7vstIvrdFXswaVQFrv/cmLzv+c1JI/DAV4+D08FkZ1K0meJcVUWGWv2n2OdCwOtCKJrMmBCpCmXZ0Yhr8Ltdps9XpRgG1hU5xw0slvcD9TMeM6QUIyr9eGGheTW364zPu25vB5bUtmD17vaMdrjc75aOstelV4qylqSz1tx3Wk6u8oAbKa7XmPa6HKbrcmCJT4reqiIPPv3VZJmhFUJ5ZFUgoxPzwrWn4r2f6WnRplAcJ4wsR6nPZeoQCtTr3uXQR4+LPC4wxnDphCHy+IoygOKe4/c4ZSfATsyKdvgwZeRqTHURRlUFMHODLpQZSy9SdPPLKxCJazjBmCw6dVUdTh9bZeos22FdzGfCsDJ8+POzs2wNjK4OyMnOokTgazecjrdvPFNm+9W23JXDLReU+l04aWQFNtQHsy6HfbDQ71fmKwu40RiKIZniJoEGpHtZQggNKfPjmyfrJ8WlE4aYelCCM8ZVo/b+L2DsgGJTw2rXwxpt6al6XQ5UBtxoCccQT6YQT6Zkw+n3ONFh1CgUqHlcl4PBY1P1QiUST8rP0pnQlKoNevSC2zjKdpP5REZVbWytNxGXg2FUVRGOGVoq606uNEp+5evt+hWhk0tUZxOAomHOt+DIkCwixvpdqb1v8Z6qw+522DV4Dpw1rloeb/EaYgb16X/6RK6SxwzXptzvztvACcptHGW1fPUT352EKd85KedrqJP5xOtZhZ8Yzi3yuJQqFUIoJ003z2OHlWFzfVBGLwQOB8NPzxtnEg2iAzS8MnueFEjHTg6rLsrrelod5WxMMBp8sf3frzxBrlQ4sNSHr500HP/f3rlHx1Fd6f479eiXpNbLkiVbsiXjp/ATC9lg8zAYY2IyYGPjZMCTYGbIGsJKyAQCSRxYCRASQrjMzb1DcCa59yZ37oRJJit3BTLAMInz4DFgSAIEhwQwdmyMseW3sKSWuuaPqnP6VHVVV3WrH9XS/q2lZat1ulXq03Vq1z7f/nZcd3ftkGGM4Xd3rMFjn7A7X07z+ZvyJRExA/bGmgg+s3YudFVBh5BeRG3dKvln4dZL52D3vR+wvWetySjeOzlo6xzp1YY3CLKFWn1cFzeo9121EL+94xIsmdYIxphNpzsjR3YupitYMXNSVvEuD+T6T5nNahqsqn3AlFf8t82LcINPQBr0vHKD66zdivk4zmvHyaERtDfEA/3er25ciKvPNrWyfE3mN4UPfmgJlnU32T5T9oyymcnkeu1ERBVa0HePm8FnXczU8xqGgfdTo4hHFM/dQKfMTJYjyVI7xhjWLZhi/T8z/vIF7ZhUG8HP/vAetv34Vdzz2C6R6ebXkIZERHwGo5qClrooBoZHcXIwhWfePAzDMLKK+ZzJC35cz7zZj0mWfZvM965fhnvWzxfX6RUzJ+Hq3g6sOdPNoMtEl+o9pjcn8NFzu7Dj1lWuN5LyYxFVwfTmGtfzXmSUpaJo+fc54d7OclKAMYYLZrfgmTcPm8kzTcXqnsk4b9YkUXwoWxZutj5Ludi6sgt3Xzlf7IQMpkbt52mLc7dbFTto/GY3EdGwqLNBvBd+SQ9nsjAZ03He7En40NmdobeMy516mQA0JiJCZ+jMXj57+8WuHa+CIgePbgvm+iVTsfPtI6KxgaIwNNZEcHQgJbam+B3pyKiBP7x7El/8yWvi+bKLBfdRNl0v3APl1Khh6VGZrTBQE9ILs6WrHGBGXALlU0KjLC+29vdOvqNsTcYwtSEuigeKJ71w//ieTo2iLqbj9PCoq6UZX6Am1UZw5wd78NNXDtj0WPVx3eYFKmdc+GfEzfXCCWMMjQnztfgFyLmY1sU0TG0w7fCcbaNz0SBplHmGSc7cyIVJXvB5iGkKrl/ZjZFRA9cun2Ybw6UY3EcZAD7yneex45YLzYyydM7wlrunrWBG5ubVs23f8/dxkkcwOrXBdErZurIbdz+2y9ONREYU83nsQjxx8/k4cPw0nt99BM/vPuLZrhwwJTB+gTJgBuVnTqnHc5+9GJu3P4s9/e8XPVB2g2eUW+qiUBWGS3om29qJu603LbVRS3rhvS2eD/LFXFWYWKvaG2KuO2hA9gVYPoaYruIza+dm/ZxLpMzWyWlLL6/hxOAI4rqK9UvcJTDFgp9ruXYq3Bxq6uP5X1752svf277uJjzysXNsY2Rtf01EQyKiCU3w7ZfNxfyp9fjVnw6LjHJbMmbVtxgYTRtIWHpajvxZce5ezZTkTs5z9Zpl07DrwAncdNFMRKwdTUVhuGB2K57adRCp0TQGhkdEB73GGtNRI66rwis7YgXKgGkz9/f/8Sfcu2GBr/SCb/vvP3Y6KzPMX/eaZfYd3/s2Lsoa5ySmq/j+Dcsxs7UWmqp4rgHy+6drDNvWzctycwAy2X8hvbAFytnn6HUruvD0G4dFUyXOzNZaDKbS2H/0NOIRU7Z266VzhDf0xfNa8c/P78WyGU2iGVcuWutiuHb5dLy45wj+x8/fwOnUKBoTOnSVITVqYHFHA96SGjnFrJ2WKfVxW6GtTEeOIlogW7qUjOs4a1qjsE4MMxM+UJbvoJ0LYVt9zNYdzYtnbr/I1VPRT1A/rz2JL10xH5d/49fiscZEBKeGMi17+R3pBxa0Z3WROiTZI8muF6MunfHEOEWBpjLTk3mEd+bLFPO9ddjeeZCf4JrLSS0Hsc73zrkILJ7WIBZH34yyLgfK/tILDmOmpZFwwEiNoiaqZgXK/PtJtVFct6IbacNeuOAsMnNbLOW/z+294ZielUxk9pwV+RFNEYtuLutAt9flx8YzTPkGPVxyoakKNNW0XHNiyNILaY6ff/uIrdgUyFhfpQ3/7ALX+/ObrWXdTRhMjYpGI//018vw6Mvv4LoV3Xjh7SP4i0XuRZIy/PPgzO5x5rTVYU5bHRoTEfzDjjdzSjk6mhJZ3su5aKuPCUlSZxkC5Zqohvs2LsRyyxP2W3/V6/uc1roYXtl/whYoj8XD1Jnhv+PyHsxsrRXFzm7IvsOcVXNbUR/XsdVDGsF3Y3hGOaYr4DGJc1euFIhmPDnWc7ddDDd7xKA47Qy9Xrc2qiEhefrGNFVoibm7ztRG80acZ+14/wC/1waAM6SM8tLp9oCmsymB/7O1D076uhvxry/tAwCkjg9iv5Ulnd6UwB9TJxHVM64TpvTCnF/ekfb7z+/FrMl2BxrnZ60tGUNMVzCYSrsWO4+F5TOafcc4pRduUgPAXswH2HdL3WRb86fW47nPXZz1OF+L3jp8CjHreXI9xaKOBrz4hUt8j9sJP7cGU2mx+3P8dAqtjrXPtJBlWJ0jAeO35jtv3p0NesLMhJdeyLoZrwusH9zU34lXxtM2xrH48mPgVms8S/OXy6YJb1aObH+jSQ1HUh7SC8AM6riDhiy9YJY9HL+L5EEbP8HdMlRyEOv8OzSHHGGJdNefjz1crrHOE40HdaIDWyrtenHj/ppce+zMhicd7WWbXQJlOTjOaeNWE7EX4jgyNrqq4CKr2v1zH5iHoPDPralRNv9GN2P/XMR1JacGHJBcLyIqpjTEsdHaftt14AQMw77wy7q3XBd6IJNR5rUAG5d2YNvlPeLnXZNqcNNFs6AqDA9v6cW6he2+f09GepH7vFvU2YBf3HphVsZJ5pvXLsVdV873/Z0yfZYuMqjueqxc3dtpawPtx6zJtTh8agg/+s1+Iem60sOlJSj/9/pleOgas1FSY00EH181M6dExs25ZHIyht/duUa4VTjh58+7JwbN9ueaKjSu5chG1YuMsve54pZRdq4j+ZDr/JHP2RorUOY+yVFdEUH7awdOYAbvSmnt9ADm3+EV2DkLMmXphTN48kJ+TmrUwCv7jiGiKmhviJuFhNLvjkcyGeVX9ps7q7/bdzwr8eRsOMIYE5IO2f+6XETlYr4ciRKnRlne7QrqugRkdpB2Hx7I7GpavROA7BuJoPBAma9dLXVRNNVEbHFRV3MikIQo3xvDsZwf5aZ6QvoS0SLpcvy0jflS63PBBlwaPFgnFC9ukAM9Z1Ajt4k1TxpmFvO5NCWRx5kOGnILa2ZbXFWFYVZrLd46NCAyfmmX4Fu+I3ZqlJ2LR59UUewvvQimUfYqruGZk9OpUeGMIcNlLfwC7MyGO094p+sFYC9udC7iMp+4aJZrkxhOajSNbet6cOOqmYG2+jk8o9wsZZS9Wtl6cc4ZzchxaAAy865ZzUzu37QIv9l7FK9aBviyblPOwHZ4ZGv7upvw/O4j4nP+sQtmIBnTsH7JVOw6cNL1OUHhW3tBbnjd6gtk8pkLzv2bFuGTF8/2/FxWmo+c24W9R97Hd5/dg5qohle+eOmYX3OlhzeqF14BWi74jSrfkZLX6UWd2QmKYsN/X655dZNlFJJR7rCyv0GDiJqohpqIJjS/cV21ff4XdNSLZlV898CrkRFg7oz88tZVeGrXQXzp0dcww9oB8LP0lJnh2DXYueco2upjuGLRFMxrrxONvABYrbrN4zkotfw2A0JFBMPOYj4AuOuKM/HS3mOeDalKCb8u8UyrF1muF9J66aZR9oI3GzLlk5nXeO5zF2fpufOhJqrhiZvPF3Kxc89oxuFTQ9iwZCp+9NI+bN/SG3jXhjGG29bOtTleeXHdii6cm2PnKWyEc0UvI3KGo9CMshe5ij84Xi2DuUG8nDV1LnD7pUBZV5kotshVoKMrZuviIclBI6JmPJ9f2X8cnY1xYQXG71jdYjB7QYhDo+zIKMu+1H6uF3FbRjlHAY3Hgi8X87ltn29b14OGhI4LLI9N5xwkHdpCt4yyrgTLKLsFEg9uXoxHXvgznn2rH/0Dw4hoCpq0/AKzOW11mFQbxdz2JAotU1q/pMNX3zm9OYG3Dg/YsrQzW2tFS1X5MynLlLwyYt/a0osX3j4iNKxRTRVuBH6fCz/cGo6Uk0REc21aEhZ0VcGNF87Ed5/dY/PYLQeP33xewQU7MV1FXVQTbe2juip2xerKkJXia2CupFo8kinWShsGBlPpggLlH398Bd47Ebwupi6mZbkEtdZF0V4fw4Hjg+hpT+LQySGcTmUyynx9/XBfJ1bOzNabTmtOYOvKbmy1PLy/89FezGoN/rl2WgDuO3oafd1NWN0zGat7JuM3e3fajrcxEYGmMIykDbOPwMAwdh8ewLz2JHZZzSjcMqZbzunClnOyHi4L/DPhvM45SeYo5svn5qOpJoKopmBI8rPmj48Vec2SawSe/NQFeb8Wt8Xz47a1c313M8PEhA+UZUeDYl9gefZkfY7tTae0gJ9Q3M5HzizwD1bCspiRpReGkTkpj74/LC4kbscUj2RLL3iQ8do7J9Db1ShpSM3f6fTXdR57luuFI6MsB5N+W05BpRde20387x5MjWYFwTetmolpzQlbYYfz2J0XX7eLsZwZ81ssTeyKWQAAFZRJREFUnVy5ZCqaayNmoOzShjcInU0J7Ny2GgCE73YpeHDzEjy3u9+m5z2jpRZP/P4gAHsmjTfMUBXmWfhUn9A9dW6xAm3KOEFdLyYybfUxfGbtHFf3iVIyt81dVhGUtvoY/nTQ3HGIaQp++ZlVGMlRi1FM+FqWGvHesYnr5mcvopmOEoOpoYIC5Um10ZwNVZzURDVbljIeMdu337JmDj79g9+ht6sJv3j9PTNQtm5U+M3tvRvcO546uWiuf2GwH7KOWA4Q47oKRWHo627CM2/2o6+rSTg5yMmXXLt2lcCtv4AbvN5FSC+kdTGfjDJjDO31Mbzd//64WN/85Jdho7qOtgTIwVYp7nD+cNda4cvqhnPbhmdQeaAsZ5R58Mr9dt+ROusMj6TFSXlkIIUpDTE89XfZd4RCozxsl17wIOPU0Aiaa6LiOPgH2im9iFidhjjZ0ovsj9Z3t/bhw32dvnoqexOIYB/RruYEblljOivw7bpBR9OX7VuW4pZL3RpAJLFxaYewnHJm7t1uEoIW83nBtYBB3Bz8KGVRRH1Cz6rAll0dnDeXbclYwRpdZ6fKfOlsimPdgvZAxTgTmRsvnCkabFQLc9rqRFOeeERFS13U5nVfSviNcK7AnAcvuqqI5EbQzpNjIaHbi2z5zeZVSzvw/OcuxtLpjYhFVBgGREa+HEVUl545GQrLuHe0SXMlr+n8mnvRXLNOIxnXxNoa1VQhOShUg1sqRHdXn+uTU3ohX1v8gmwn/POeb2ImTPA6q7HYNVaCCZ9RlvFrVFAI+QbfmYyymSWsjdkzdoCZkdVV2NwchkbSYoE+OjCM+rjueiLqilnA1T8wLKQXuqrYFttkXLMF5UC29MIZwNY43ju3DMD5s1uyWor6EVTT+PNbLsTuwwO4/8k/ZqQXw6O2i4KXRCIR0XD/pkV4+o3DOHB8UDQH4aQNAw9vWWpzrLB15itgEZ89uRYblkwV25tjoRDd51iQM17O7MYN588o6MYBsPu0FvR8TcX/tArLiPHFvPYkHn3Z7Gg51p2HfOGSIi/LOyCjoY2oisgkj8X1IijOZidcAgJkiu94cPboy+8gGdNcC8+LzUPXmB7u3/71btzz0122gJIHjRFVEWvy5rM78dxb/bh+5Qw8/UY/9h87jbqYhjOnJHHg+GBJd80Kgf8NfgFfVjGfuKHKrW124/JF7Xj2rf4xOdVUmv99XZ/NdadaoEBZolLaRhm5mM/0PM6++9alBYZjZpTN6TwyMIzm2ohrAMUL9wYl6UVEVWx66rqYLoI/viA4bfKc2mFVYTa5R6HBUqEwxsT7M5gyzfW5PRzHLyvBF/OGuI7X716LTd98Fi/vO47RtJGVVfXqzBcUTVXwwObFeT/Pi7+7ZLbNdL6UyDcSzhskr7bOQai27TiifMxrz+goF5ahgE9mc28nNIXllNC1JqNorongjg/24JEX/gwg2+GmmPzlsmn41xdNCzb5HHSr6eCB8lO73sOGJVPz2vIvFL7WXreiC6rCcMXiTCtzfp7LO0h1MR3/+JGzAWRqb65YPAVnTW9Ew+Ovh67wi18rDJfdRhlnwxF+U5OP4wXnmmXT0ZiIlMWnvVTEdLWqtMkcCpRhVno+82Z/xbQ//+9vlgktrSy9cGpj+YKnKNlB/dDIqMgoD4+moSnMNdOpqQriumLzUdZUZtPyJmOacFDgi9rS6Y348cdX4KEdb+CJ3x90DWpqolKgXIHtIf7+/PTVd3HsdAppwy4JcaucluEXkKimIKqpIgD2lV6EYCvsExdneyCXiklSA5ZinjMUKBNezLM8Y6c2xG0dxMqBojBs6s3d7Symq8LH9vFX34XCgrkeFcqX1y/Al9cvAGA/B92CEPnn5ZYlaaqStWsmt3N2Y9PSDvzgxX24pKdNOO2EDR7o+sTJUkaZ1xdZnV0LXOs+sKC6JFPjBQqUATy8ZSle3ne8Yr5+8t0yX0T6Tw2jw9FjPias2jKLDM/iyhplwMxyugXKupT5FRplhcHeblsXAa+8ZbZYalfpFtQk47qQjJQro/zg5sUZs33rIvHLPx7CL/94CLrKsKZnMu57/HUAgOITKPPFj0sAuppr8Ju9x0ShjkyQznzjlVIVwFabbo0oH+31cXxt40KcNys/6VYl6GyMo7MpUTZdrbxr5uaCIAfPcpfRShERGWX3teOrVy3EXVfOD/W6KjLKPuOSjoYjCUnLTlQPFCjDvOtbUQEvRjf44jE8ms7KKPOfjaYNkT3tnlSD1w6csGmUAVjd1rJPRlVhGR/ltIGI1WxE3r6ri2kii+oMiHkA7LYgf2XDQvyvp3fj3159t2xVynLDBOex3vHBMzFTsjXyS/zyu3z+Ovesn49Lz5zs2ghBU8emUa5m5AtcseVKX9+0CAs6yru1TlQHflndsHDjqpm4zqPLYCmIqOY5OLetzjW4lAvInNZtlYCvr16BsKIwxJRwb8+LIneflHJNRMOU+hi6LN/2sUgviMpBsxUy5GAv6ahOFoGyIQXKVge9YctfkUsCzE59mYUoLumb47qK4ZE0Tg+PioBPzkok47r4XU7Nm25Fm25tevu6m8pSKOKFojCRdV+3sB1blts7r/lJL6KqPVBORDRPdwCeEVBY+Cqyy0mx5UpXLe3A7Mnh9SImCD9iulrWgJSv4Rs96gPkc7QxR0FiueDXFL/1OMyIInefJk+KwvD07Rfh6rPNmzyeWMjHQ5moPJRRDhly0wWnBzAPXtNpA4NWNx7uhzo0YvZqT8Z09A8MQ7U6qXHq46acQlWYWCwPnRoSAZ+mKsLQvC6mYVpTAmt6JqPbw2/VrRUtkLtBST58ZcMC9BdQ6RzTVQym0q4yGr+tvIjIKPsHfzyLHAZ9ciWhzAhBVJZL5k3G967v8+xQZ8sol7DAMCh8na3iOFkkU4Jc5mRJWcKS8eVrDUdUFgqUQ4YcpDn9LuNSRvmk1bKUB7LDlt44GTcDZV1VRPbXfFzDuydM2QaXTRw8PmjTStVENQyNDKMupqOzKYHtf9WbdXyHLH9nt4wykMmu5ttO2cmH+qYV9Ly4ruIYUlnZeMBfAyv8OwP4+fIsTph1dOWAdMUEUVkUheXUbstSqUrV4cjwINOvZiTMZFwv8ntenDLKVQnNVshwWua4/Ww0nQmUpzebAWtfl2nkzQNEVWE2SQBfIIdGRkVL5oMnB213tlx+4RZkcg5YTU48A2Xr5fxsc0oFX3zdzP6DZ5QDBMoKb2FavYv9WNi0tIOyyQRRBcjSizDIxHgiopoDZZ7Qyvc6R8V81QlllEOGHHw4M8pyMd/JQdO0u7Uuhic/db7oYHTwhJnx5XZKHG5+PzSSRpNV+XzwxBDakhmrJV7Q59aymXPguOlx6RUoZyzVPF+ipPDMulv3qeD2cAGkFzyjPEG30L62aRG+FkLbJoIg7Dg7jVYaXnxYxXFyYNcLJ3KtEFE90GyFDMaYyGh6+SiPpg3hh9lSF8XsyXViLA/gPnpul+25PMM6lEoL6cXwSNqRUTY78uXaFvrQ2aYkQg6wnccPmPKQSjDCJSguwb6fnFhklANIL4S2OwQZGoIgCC/CFiiPC+mFqMXJ7zrHC87JM766oIxyCBFFdVnFfBnpxf2bFuHTa+ZkeVF+d2sfjgwMZ9m3cTnF0MiorfLZqVHOlU0GgNvWzsGn18z2tvaxHvarBi4VqVHz97pmlP2kF2o+0gvSKBMEEX7CFpTxhEQYZCCFIlwvCrjMJSIaZZSrDAqUQ0hUV4HBEU/pRdowENNVV0eKGS21mOFS15GUpBe6qiAZ03BicMR2wrbURnEkGc1+sgRjLGfFLpc3jLWYr1DkokYnvg1HrMUviPY2k1GmBY8giPAStoBUBMrhOqy8EDcfBVzm4rpKrhdVBgXKIYRnjr0ajhQSg8oaZQBoro1agXLmhP38unmiI1+hKBXWKKdyaJT9AuWopiCmK4GcHLjEpVwdCAmCIArlw33TcN6scDTV4rtwVS29EBrl/C9086cmySu+ysg7UGaMfRtAD4DHDMO422NMPYDvA1ABDADYbBhG/qa4ExReTOaVUS4E4XphBcJNNRHsPjxg697n1m0vX3hGuVKuF/zXuklI/GQS1y6fjrOmNQb6PTyTTNILgiDCzr0bFlT6EARcllfNS+dYpBcPb8m2XSXCTV77xoyxDQBUwzDOATCDMTbLY+g1AB4wDGMNgHcBrB3bYU4sMsV8jkB5DFqzZJxrlM2MKw+Ki23xxYP5WJE7tuWLm8Wdn+vF9OYaXLbAvROfE7kDIkEQBBEMHlxWswc7T2blW8xHVCf5RkkXAvgX6/9PAljpNsgwjH8wDOPfrW9bALznNo4xdgNjbCdjbOehQ4fyPJTxCw+Uax3BHs/+Xrs8/2YcPMN65hTTNm5Zt+m7vPfI+wUfpxtr57fhU6tn4/bL5hb1dYPCM7zc6k6mmOsynwuVNMoEQRCBOaPVrK25ZllhTaXCQLTAhiNEdZJTesEYexjAHOmhCwB82/r/EQBn+Tz/HACNhmE85/ZzwzC2A9gOAL29vfSRs+BZWTeLszfuuayg7X5NYfjRjeeKltd/sXgK7n5sV9EDZVVh+ORqr42G0vOTm1biP3f3uxawFFMmoSuUUSYIgsiX1roY3v7KukofxpjgO7G1USrzmgjknGXDMD4mf88Y+3sAcevbWuTISDPGmgB8A8BVYzzGCUdUU6CrzNXWRytQKqGpzKa/ba2L4ebVs0Rnv/FCz5QkeqYkXX9WzECZvxYV8xEEQUwsFIXhC5f34PyQFEgSpSXf26EXYcotngOwCMDrboMYYxEAPwDwWcMw9ozpCCcgUU1FXUwvqobLrcL45tWzi/b61UAxq6w1ajhCEAQxYbl+ZXelD4EoE/mmJ38MYAtj7AEAVwN4jDHWwxhzul9cD1OW8XnG2A7G2OYiHOuEoaUuKlpSFwtyZyhulTUv5qP3lSAIgiDGL3lllA3DOMEYuxDAJQDuMwzjOIDjALY5xj0E4KFiHeRE47bL5gobt2JRzZ6VxaKYQS23h6OGIwRBEAQxfslbiW4YxlFknC+IElAb1YpeJEBa2uJ2qKKMMkEQBEGMfygdNkHw8xCeCBTzPWCMQVUYaZQJgiAIYhxDgfIEoZjZ1Gql2NlfTWGUUSYIgiCIcQwFyhMEynwWt+EIAOiqAr3InQ0JgiAIgggPdJWfIFAxX/HlJ5pKGWWCIAiCGM9QoDxBoICuFNILhTL1BEEQBDGOoUB5gkCBMorawAUA6uMakvHsNuMEQRAEQYwPqFH5BIEC5eLznY+ejWSMAmWCIAiCGK9QoDxBIHu44jO9uabSh0AQBEEQRAkh6cUEYSLbw91xeQ86GuOVPgyCIAiCIKoMyihPECZy0dnWld3YurK70odBEARBEESVQRnlcQ5XXJBGmSAIgiAIIj8oUB7ncP9k8lEmCIIgCILIDwqUxzlblk8HQBllgiAIgiCIfGGGYVT6GAAAvb29xs6dOyt9GOOOdNpAKp1GVFMrfSgEQRAEQRChgDH2omEYvX7jqJhvnKMoDFGFgmSCIAiCIIh8IekFQRAEQRAEQbhAgTJBEARBEARBuECBMkEQBEEQBEG4QIEyQRAEQRAEQbhAgTJBEARBEARBuBAaezjG2CEAewIOrwdwvISHUy6mAdhb6YMoAjQf4WI8zAfNRbig+QgXNB/hguYjXASdj+mGYbT4DQpNoJwPjLHthmHcUOnjGCuMsUNBJins0HyEi/EwHzQX4YLmI1zQfIQLmo9wUez5qFbpxU8qfQBF4lilD6BI0HyEi/EwHzQX4YLmI1zQfIQLmo9wUdT5qMpA2TCM8TKZ42GLg+YjZIyT+aC5CBc0H+GC5iNc0HyEi6LOR1UGyuOI7ZU+AMIGzUd4oLkIFzQf4YLmI1zQfISLos5HVWqUCYIgCIIgCKLUUEaZICwYY+2MsdWMsbpKHwtBEARBEJWHAuUSwhibzBj7lfX/sxhjTzHGnmaMfdp6bBpjbAdj7GeMse3MJGscMXYCzMVsAI8AWAHgF4yxCM1F6fCbD2ncfMbYv/uNI8ZGgPNjKmNsn7Ve7WCMtTDGuhljjzHGfsUY+3pl/4LxRR7nx08YY4v9xhFjI8D58UXp3PgDY+yzNB+lI8B8zGCM/Qdj7LeMsS94jQuMYRj0VYIvAI0AHgfwkvX90wA6ATAAzwDoBnAPgHnWz/8NwEK3cZX+W6r9K+BcbARwhvXzHwKYQ3NRufmwHmcAngSwI9c4+ir9fADYAOBvHc/7FwDLrf8/AuDCSv8t4+Erj/PjGgAPSs+j86OC8yGN/yGAqTQflZsPAA8AWGH9/NcAWsYyH5RRLh2jADYDOGF932QYxp8Nc+b6ASQNw/i8YRi7rJ83AzjsNq7cBz4OCTIXPwSwhzG2DuaJ+IbbuAoc+3jEdz6sx68D8HPpeTQfpSHIfCwH8NeMsZcYY1+2xs0G8JL1//dgNisgxo7vfDDGmgB8HcBRxtgqr3HlPvBxStD1CoyxswHsMwxjf65xxJgIMh/9ABYyxiYDiMK0iyt4PrRiHj2RwTCMEwDAGOMPPc0YuwnAEQBdAF7mP2CMbQbwe8Mw3rG2BVzHEYWRx1zUArgaZodII8c4YgwEmQ/GWDOAawFcan25jivfUY9fAp4fTQDuAvA+gKcYYwthZs7uZIw9B2AtgM+W98jHJwHn40sAfgDgYQD3WnUVdH6UgHyu5QA+CeDOAOOIAgk4HxqATwDoAPAzACMe4wL/Uvoq7TbBDutfFcBqmCn/a6WfzwDwAoD6XOPoq/RzIY37HoBlNBeVmw8A3wKwLJ95o6+SzkdUGvcAgKus/68E8P8BbKv08Y+3L5/5eBTAXOv/l1lzQudHhebDerwBwJPS9zQfFZoPmDeR3NXtvwNYM5b5IOlFmTAMYxTA69a3/wQAjLFGAP8MYKthGMe9xhHFxWMuHmKMnW891gDgGM1FefB4ny8A8FXG2A4Aixljd9N8lAeP9/kJZrrCJGBedF61Hv8tgGkwAzWiBHjMxxswkywA0AtgD50f5SHH+3wFgJ8GGEcUEY/3uRtAJ2MsBuAsc1jh80HSi/JyN4DbDOs2B8DtMC8y37C2Ee40DOMXLuOI4uN8j+8D8D3GmAEzK/C6xziiNNjeZ8MwZvMfMMZ2GIaxzW0cUTKc7/MXYerFhwF8Uzo/bgXwgGEY71fgGCcSbuvVPzLGPg9TDrPBYxxRGtze50sB3B9gHFF8nO/znQB2wCziexSm/MJtXCCo4QhBEARBEARBuEDSC4IgCIIgCIJwgQJlgiAIgiAIgnCBAmWCIAiCIAiCcIECZYIgCIIgCIJwgQJlgiAIgiAIgnCBAmWCIAiCIAiCcIECZYIgCIIgCIJw4b8AVBqLdOjtmN0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the dataset\n",
    "ew_excs = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn').content\n",
    "raw = pd.read_table(BytesIO(ew_excs), header=None, skipfooter=1, engine='python')\n",
    "raw.index = pd.date_range('1926-01-01', '1995-12-01', freq='MS')\n",
    "\n",
    "dta_kns = raw.loc[:'1986'] - raw.loc[:'1986'].mean()\n",
    "\n",
    "# Plot the dataset\n",
    "dta_kns[0].plot(title='Excess returns', figsize=(12, 3))\n",
    "\n",
    "# Fit the model\n",
    "mod_kns = sm.tsa.MarkovRegression(dta_kns, k_regimes=3, trend='nc', switching_variance=True)\n",
    "res_kns = mod_kns.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:1286: RuntimeWarning: invalid value encountered in sqrt\n",
      "  bse_ = np.sqrt(np.diag(self.cov_params()))\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in greater\n",
      "  return (self.a < x) & (x < self.b)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in less\n",
      "  return (self.a < x) & (x < self.b)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:1821: RuntimeWarning: invalid value encountered in less_equal\n",
      "  cond2 = cond0 & (x <= self.a)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>0</td>        <th>  No. Observations:  </th>    <td>732</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>1001.895</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th> <td>-1985.790</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>14:59:00</td>     <th>  BIC                </th> <td>-1944.428</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>01-01-1926</td>    <th>  HQIC               </th> <td>-1969.834</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 12-01-1986</td>   <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0012</td> <td>    0.000</td> <td>    6.675</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0040</td> <td>    0.000</td> <td>    8.477</td> <td> 0.000</td> <td>    0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 2 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0311</td> <td>    0.006</td> <td>    5.539</td> <td> 0.000</td> <td>    0.020</td> <td>    0.042</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.9747</td> <td>      nan</td> <td>      nan</td> <td>   nan</td> <td>      nan</td> <td>      nan</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0195</td> <td>    0.012</td> <td>    1.681</td> <td> 0.093</td> <td>   -0.003</td> <td>    0.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->0]</th> <td> 2.354e-08</td> <td>    0.004</td> <td> 5.61e-06</td> <td> 1.000</td> <td>   -0.008</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->1]</th> <td>    0.0253</td> <td>    0.018</td> <td>    1.408</td> <td> 0.159</td> <td>   -0.010</td> <td>    0.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->1]</th> <td>    0.9688</td> <td>    0.014</td> <td>   68.322</td> <td> 0.000</td> <td>    0.941</td> <td>    0.997</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->1]</th> <td>    0.0493</td> <td>    0.040</td> <td>    1.223</td> <td> 0.221</td> <td>   -0.030</td> <td>    0.128</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      0   No. Observations:                  732\n",
       "Model:               MarkovRegression   Log Likelihood                1001.895\n",
       "Date:                Tue, 24 Dec 2019   AIC                          -1985.790\n",
       "Time:                        14:59:00   BIC                          -1944.428\n",
       "Sample:                    01-01-1926   HQIC                         -1969.834\n",
       "                         - 12-01-1986                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.0012      0.000      6.675      0.000       0.001       0.002\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.0040      0.000      8.477      0.000       0.003       0.005\n",
       "                             Regime 2 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.0311      0.006      5.539      0.000       0.020       0.042\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.9747        nan        nan        nan         nan         nan\n",
       "p[1->0]        0.0195      0.012      1.681      0.093      -0.003       0.042\n",
       "p[2->0]     2.354e-08      0.004   5.61e-06      1.000      -0.008       0.008\n",
       "p[0->1]        0.0253      0.018      1.408      0.159      -0.010       0.061\n",
       "p[1->1]        0.9688      0.014     68.322      0.000       0.941       0.997\n",
       "p[2->1]        0.0493      0.040      1.223      0.221      -0.030       0.128\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_kns.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the probabilities of being in each of the regimes; only in a few periods is a high-variance regime probable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, figsize=(10,7))\n",
    "\n",
    "ax = axes[0]\n",
    "ax.plot(res_kns.smoothed_marginal_probabilities[0])\n",
    "ax.set(title='Smoothed probability of a low-variance regime for stock returns')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(res_kns.smoothed_marginal_probabilities[1])\n",
    "ax.set(title='Smoothed probability of a medium-variance regime for stock returns')\n",
    "\n",
    "ax = axes[2]\n",
    "ax.plot(res_kns.smoothed_marginal_probabilities[2])\n",
    "ax.set(title='Smoothed probability of a high-variance regime for stock returns')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filardo (1994) Time-Varying Transition Probabilities\n",
    "\n",
    "This model demonstrates estimation with time-varying transition probabilities. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn.\n",
    "\n",
    "In the above models we have assumed that the transition probabilities are constant across time. Here we allow the probabilities to change with the state of the economy. Otherwise, the model is the same Markov autoregression of Hamilton (1989).\n",
    "\n",
    "Each period, the regime now transitions according to the following matrix of time-varying transition probabilities:\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00,t} & p_{10,t} \\\\\n",
    "p_{01,t} & p_{11,t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "where $p_{ij,t}$ is the probability of transitioning *from* regime $i$, *to* regime $j$ in period $t$, and is defined to be:\n",
    "\n",
    "$$\n",
    "p_{ij,t} = \\frac{\\exp\\{ x_{t-1}' \\beta_{ij} \\}}{1 + \\exp\\{ x_{t-1}' \\beta_{ij} \\}}\n",
    "$$\n",
    "\n",
    "Instead of estimating the transition probabilities as part of maximum likelihood, the regression coefficients $\\beta_{ij}$ are estimated. These coefficients relate the transition probabilities to a vector of pre-determined or exogenous regressors $x_{t-1}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the dataset\n",
    "filardo = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn').content\n",
    "dta_filardo = pd.read_table(BytesIO(filardo), sep=' +', header=None, skipfooter=1, engine='python')\n",
    "dta_filardo.columns = ['month', 'ip', 'leading']\n",
    "dta_filardo.index = pd.date_range('1948-01-01', '1991-04-01', freq='MS')\n",
    "\n",
    "dta_filardo['dlip'] = np.log(dta_filardo['ip']).diff()*100\n",
    "# Deflated pre-1960 observations by ratio of std. devs.\n",
    "# See hmt_tvp.opt or Filardo (1994) p. 302\n",
    "std_ratio = dta_filardo['dlip']['1960-01-01':].std() / dta_filardo['dlip'][:'1959-12-01'].std()\n",
    "dta_filardo['dlip'][:'1959-12-01'] = dta_filardo['dlip'][:'1959-12-01'] * std_ratio\n",
    "\n",
    "dta_filardo['dlleading'] = np.log(dta_filardo['leading']).diff()*100\n",
    "dta_filardo['dmdlleading'] = dta_filardo['dlleading'] - dta_filardo['dlleading'].mean()\n",
    "\n",
    "# Plot the data\n",
    "dta_filardo['dlip'].plot(title='Standardized growth rate of industrial production', figsize=(13,3))\n",
    "plt.figure()\n",
    "dta_filardo['dmdlleading'].plot(title='Leading indicator', figsize=(13,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The time-varying transition probabilities are specified by the `exog_tvtp` parameter.\n",
    "\n",
    "Here we demonstrate another feature of model fitting - the use of a random search for MLE starting parameters. Because Markov switching models are often characterized by many local maxima of the likelihood function, performing an initial optimization step can be helpful to find the best parameters.\n",
    "\n",
    "Below, we specify that 20 random perturbations from the starting parameter vector are examined and the best one used as the actual starting parameters. Because of the random nature of the search, we seed the random number generator beforehand to allow replication of the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod_filardo = sm.tsa.MarkovAutoregression(\n",
    "    dta_filardo.iloc[2:]['dlip'], k_regimes=2, order=4, switching_ar=False,\n",
    "    exog_tvtp=sm.add_constant(dta_filardo.iloc[1:-1]['dmdlleading']))\n",
    "\n",
    "np.random.seed(12345)\n",
    "res_filardo = mod_filardo.fit(search_reps=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>dlip</td>         <th>  No. Observations:  </th>    <td>514</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovAutoregression</td> <th>  Log Likelihood     </th> <td>-586.572</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 24 Dec 2019</td>   <th>  AIC                </th> <td>1195.144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>15:01:25</td>       <th>  BIC                </th> <td>1241.808</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>               <td>03-01-1948</td>      <th>  HQIC               </th> <td>1213.433</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                     <td>- 04-01-1991</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>approx</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.8659</td> <td>    0.153</td> <td>   -5.658</td> <td> 0.000</td> <td>   -1.166</td> <td>   -0.566</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.5173</td> <td>    0.077</td> <td>    6.706</td> <td> 0.000</td> <td>    0.366</td> <td>    0.668</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.4844</td> <td>    0.037</td> <td>   13.172</td> <td> 0.000</td> <td>    0.412</td> <td>    0.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>  <td>    0.1895</td> <td>    0.050</td> <td>    3.761</td> <td> 0.000</td> <td>    0.091</td> <td>    0.288</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2</th>  <td>    0.0793</td> <td>    0.051</td> <td>    1.552</td> <td> 0.121</td> <td>   -0.021</td> <td>    0.180</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3</th>  <td>    0.1109</td> <td>    0.052</td> <td>    2.136</td> <td> 0.033</td> <td>    0.009</td> <td>    0.213</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4</th>  <td>    0.1223</td> <td>    0.051</td> <td>    2.418</td> <td> 0.016</td> <td>    0.023</td> <td>    0.221</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0].tvtp0</th> <td>    1.6494</td> <td>    0.446</td> <td>    3.702</td> <td> 0.000</td> <td>    0.776</td> <td>    2.523</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0].tvtp0</th> <td>   -4.3595</td> <td>    0.747</td> <td>   -5.833</td> <td> 0.000</td> <td>   -5.824</td> <td>   -2.895</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0].tvtp1</th> <td>   -0.9945</td> <td>    0.566</td> <td>   -1.758</td> <td> 0.079</td> <td>   -2.103</td> <td>    0.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0].tvtp1</th> <td>   -1.7702</td> <td>    0.508</td> <td>   -3.484</td> <td> 0.000</td> <td>   -2.766</td> <td>   -0.775</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                         Markov Switching Model Results                         \n",
       "================================================================================\n",
       "Dep. Variable:                     dlip   No. Observations:                  514\n",
       "Model:             MarkovAutoregression   Log Likelihood                -586.572\n",
       "Date:                  Tue, 24 Dec 2019   AIC                           1195.144\n",
       "Time:                          15:01:25   BIC                           1241.808\n",
       "Sample:                      03-01-1948   HQIC                          1213.433\n",
       "                           - 04-01-1991                                         \n",
       "Covariance Type:                 approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.8659      0.153     -5.658      0.000      -1.166      -0.566\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.5173      0.077      6.706      0.000       0.366       0.668\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.4844      0.037     13.172      0.000       0.412       0.556\n",
       "ar.L1          0.1895      0.050      3.761      0.000       0.091       0.288\n",
       "ar.L2          0.0793      0.051      1.552      0.121      -0.021       0.180\n",
       "ar.L3          0.1109      0.052      2.136      0.033       0.009       0.213\n",
       "ar.L4          0.1223      0.051      2.418      0.016       0.023       0.221\n",
       "                           Regime transition parameters                          \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "p[0->0].tvtp0     1.6494      0.446      3.702      0.000       0.776       2.523\n",
       "p[1->0].tvtp0    -4.3595      0.747     -5.833      0.000      -5.824      -2.895\n",
       "p[0->0].tvtp1    -0.9945      0.566     -1.758      0.079      -2.103       0.114\n",
       "p[1->0].tvtp1    -1.7702      0.508     -3.484      0.000      -2.766      -0.775\n",
       "=================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_filardo.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the smoothed probability of the economy operating in a low-production state, and again include the NBER recessions for comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2CMDLAHwXwEsZY4bIjcwL04s1XHPuBKolBU+ezDZc4+DMGkYrKj7+hguhKoS/+taRTLen1xydq2H7eLnF664phPVVFbMrYovip+yi+FhIUXx8zvrZ1vFq7PWWVUJN3pklXaBhmPjqE7N40e71uHDzME4sDGZRzO1JbqUYAIggtJAbJHiBqlDTltIwxe3LR44v49yJCjaOlABYSrEhj5WkRwjz/jLGjjPGbmKMzYtaZ55gjGF6sYYt66u4cMuoox5mxcGzq9izoYqtYxVcdc46nF1uZLo9vebIXA3bxyttr08MlTAjuCjebz8AnV2uY6Xuv+7j81ZRvM1HKQ6irCnSPiHpCnc+u4C5NR2vuWwSW8fKOLVYH8gisKkUtxbFKhHk42hnND3Fzf2qC5TBarqJsWpzBFCh5ntKJN2mLyfEdYP51QbqhonNo1ZR/FSGRTFjDAfOrGHPBqsA40NYg0LDYDi5WMf29e1F8eSwhtlVsQ8I+08tgQvSXBH2cnzOsq9sW5+gKJYT7SRd4ranZ7FxRMO1O8cwNVrGSsPEQm3wzrW6zpXi1lsdkTWBVpKcpqeYHFtKQ6Dp12AM7uh2RSF5rCSxOHh2Fb/6haexf7rzORSyKI7J6UVr8tam0QounhrF9GINM8vZDEmeWdGxVDewZ4M1VK8pg1UUn1pqwGTwV4qHNaGeYt0w8cz0Eq7eOQEAOBJgoTg+t4rx4RKGyu2NOoIoqQrq+uAcN4kY3nvLPvzNd0+FLvPEqRU8b+s6qAph61gZAHB6abBGk4DmRDuvUqxIpbhjmp5il31CoFJsmpaSz1GlUiyJwcnFOn79P57BQ8eXUqXt5LIoPrFQx59/8xAO52jy2Gk70WDzaAUXbrEmADyVka/42RmrGD/PVoo1haAP0DD8cdsf6acUTwxpQj3Fh2ZWUNdNvOTizQCCfcUn5tcSqcQAUNGkUixJhmkyfOHBo/jq/nms1P0rkflVHccX6rh4i5XfOTVqFcUnFwevKA6yTygEDKCbRAjuSLay4ykWdx0zGYPiqkwU6SmWxODbB+Yws6LjvA1VfO+5hY7tYrksiv/lgVP4z30zeNtnn8KBM2KbMHTK9JJVoG+2lWIAeCokoovz1cdO4tV/ewfee8s+LK6JuSk9O2sV6EVRimu6gQ/e+jTWBMkJx+at/eivFJewWDOEeXWPzFjDMNfunkRJpcAEiuNzq9iWYJIdINMnJMl56tQi5lYaaBjMmaUPAGeWG3jKjl17yh46vHizVRRzpfjUQCrF/vYJhUgmGnSI6Ypk0xSuFIvbl5Z9ovkQo8hINkkM1hrWSfLqSzfg+EIdR+Y6i2bNXVG82jDxtSdncP25Y1jTTdz2zFzWmwTApRSPVbFptIKxqoZnpqOzij9732E8dXIRH7/zWXxnv5imH6cWGxirqs5kBC3nebcfv+NZfOAb+/Hpew4LWd+xhTqGSwomhto7C/LX5tfEFOBcgR8qqdg2PoRjgZ7iVWxNqBSXVHI8jxJJHO59dgaA5Uf/5v5ZfOHhadz00Gm8+dNP4hc+9xS++NgZPGlneF+02TofRysqhkvKQBbFQUoxySH5juH7TVXIedgQOVJpMo99QkaySWJQ000QgBv3rAcA3PVctGjpR7b9in247cACVhom3nrtFM4sN/BYThpTnF6sYaikYqSsgohwzsQwTsyF2ztquoF7Ds7ghy/egq8+fhKzK2I8yAZjKLlmIpRyrhTzQtIbi9Qp82sGJodLvq3HJ4atU3pOUAckvl8VImyfGMLR2XYD/0pdx8Kajqn1UimWdJd7nj2Lc8aHcOEGDbc+PYdbn7ZEg3MnKrhw8xD+121HsHFEw/b1FYza7eiJCFNjZZxaGryuYA2f5h2AnT4hP3od4Uy0c6VP1AXuTMP0TLST9glJDGo6Q0VTsG19Bbsnq/iPx87gxy7fmHg9uVOKb31mAbsnq7h8ahiXTQ3jiVMruXhKnF6sYfNYxSnEzhmvBqqGnO8fnsNqw8CrnrcVgJVgIQLTRMvwkqoQjBxf4WftCYnjw2Uh6zMYc4btvHCleG5VjFLM96umEqbGhnBqvv1BqGYP2wwnmGQHAGXpKZYkgDGGe5+dwXW7J/Hqi8dx/sYq/vq15+Hzb7kU//QzF+P9rzkP1587hjPLuqMSczavK+HM8uAVxUH2CZlT3DmOpxjuSDaRSjGDorjtE1LVl0RT001UNOu8+a0f2o4jszX8zR1HE68nV0Xx4loDj59axQ/uHgMR4bKpESzVDRyeFdu2txNOL65h82jTw7p1/RBO+BRIbu58+gxUhfBDF21CtaSIK4o9ExFKKsFg+R1i4gr5SCVZ0RiEaaLl73czOWwFvotKoNBtM5uqEEarGpZ9Jjfx/a4GFOpBlFWS6ROS2ByYXsKZpTqu2zOJK7cO459+5hJcu3MM56yvoKQq0FTCn71yF374gnG88pLJlt8tqcpAqm3BE+2kUtwpTvMOhZwRS5HNOwzTSpzgqDKSTRKDNd1EVbMKg2t2jOLHLt+ALz12NrG1NFdF8fcOnIXBrN70AHDZ1AgA4LGT2VsoTi3UsHm0OTy+bXwI86sNLNeCi6+7D57FldvXY6xawvqhEuYE2SdMtCrFXDXNawLFrN1YRNRkCcPjOXPTNaVYIQyXVd/mHYYznJi0KJbNOyTxufug5Se+bveGwGWGyyr+7JW7ccOu9S2vKwOay1t37BPeiXZSfeyU1uYddk6xYKVY9SjF8jIpicJSipuf850TVTD79STkqij+9v5pDJcUXLHVKoZ3TlSwrqzir799FL/4uacy2659xxfw7JllXLVz3HmNJw2cmA+2UBybW8WeTesAAONDZYH2iVbPldaFp3WRcKVYlJJtXTT9fzZcVlBWCXOCJtrxolhVCCMVDQ2DoeZp38T/rKBCPQhpn5Ak4Z5nZ7BlrIJzNwwn/l2FCPm8OnSXhv358p9oN4h7JD2tzTvE33tMhvb0CXmsJBFwTzGHq8ZrCUdjc1MUL9V0fOvJ07hq27Dz9KkQ4Y1XbcJYVcO+UyuZ+Wb/+e7nUC0peP0P7HBe4+18jwVMtjNNqy30JttyYSnFouwTrQWYZl+Y8uorFl0UeyN73BCRlVUsyD7RVIoVxzO8UjN8l0nonkBZVVCTRbEkBpaf+Cyu270h8YgEwJXiLmxYzqkbDCq1W5vkRLvOaaZPuJt3dG+inWWfELZ6SZ9S002UteaJw/3FSYWnXBTFz5xewps+cQ9OL9bw6kvGW372tuu24nXPs2YQZjHUvLDWwM3fP47XPv8crLf9qgCw1U4aCGr7O7tSh24yx4e8frgkTCk2WIB9IqdXeX7cRG2ed6Khl+GyijVBUWe6WykuW9aMZY+Fwu2xS0JZJRhmfh9mJPnh0NkVnFqo4drdk9EL+0AEmAOoFTcM5ogsbkg27+gYfrki6mIkm3ei3QCeu5Jk1I1W+0SlQ6U480i2v731afzvb+xHtaTgQz97Nc6rtGf/OrEvholqqbd1/IHTS1htGHjpJVtaXt8yVoVCwImAopi3heY+5PGhEh4TVBQzxuCuCZ3JDjk0XrlneIsq/qyLZvDPVUWgf9lVFA/bEwW9ncT4e4UV6n6UNfF+PEl/8uixeQBw2o0nRSEayCKwYZht1gnAUop1KT92hCMCoDlKKdY+0R7JJg+VJIqabmLCJVzyojhpL4BMleJ7n53BB765H6+6Yivu/L2X4BWXTfkuV7EroFoGM/X5BaCste6qkqpg82g10D4xzYvisS7ZJ1ybwy9MeVSK3WkNIu0TYf5dkbmWvkpxzV8pDivU/XA/7EkkYfALe6cJLoM6WaluMN98dNm8o3NYi1IsXpAx2zraSf+3JJqazpxaESiop/jdNz+KHRPDeN9PPg8b17W37OWUO/SGiIC/pV/c1rbxauBEu6ZSbP1d48MlrDaMtklaneC9aHSj1aYozi414/SETbQzWWAkG8Bzm4W8FQxbotDsiXZAu1LMC/CkSjH/AMsGHpIoOj3HOJZSPHjnWZB9YlD3hwgMlwjQjUnehtl6v1UV2bxDEs2abqJacnuK+f21IErx8blV7D+1hLfcsMspNoLgvqUsWuI2J1H5FcVDODobVBRbCjK3T6y3G1eI8BUHeYrz6E09s9SMoRMZyRZWHFiqmHilmE+08yrFrMOCxXnYk62eJRGYrvOwEwY1gqxumL5KseVTlXSCoxSjeW8WOtGuzT4xmJNEJcnwRrJxq21hlOJ7nj0LALguxsSRsjPMnJ19wu9etGfjCI7Orviqv6cXahitaBiyC6n1Q5bXZV6AhYKx1u3J80S7rijFnhxLL5oibma5YTRzigOV4g49xSWpFEtioqcuigczbaFuMF9P8aDuDxGYLhGg1AXrnncitYxkk8TBWxRXOhSdMiuK7312BqNVDZdsHYtctpxh8WCE3Iz2bFoHkwGHz660/Wx6sYZNY01LyDgvigUoxV77RDdicURxdtmlFAvzFLd2PPKikri2182hQsKI/YCzJMhTXJaeYklMOu2ayBlUX6Y10S4ofWLw9ocInOYdinU+KiT23uydaGfZJ4StXtKnBHqKi9LR7p6DM7h212Ssi3yWw8yOl89nO8+zG3McmG5PzPC2heZKsYjJdm0T7QqjFItZp9W8JMQ+oYibVGSYlipNRBh2lGK9bRmgk452/LzO33GT5Avn4TyVp1jkFhWDoIl21mTcDDaoD2imT1j7taSS0Eg2gzHnngY0R0UH8aFOEg/DZNBN5qjDgDt9ogBFsW4yHDyzjOv2xMvcbCrFvS+KzZCb0e5NVue9A9PtbahPL7a2hR63o0LmRHiKTf+JdnksihddqqrYSLbg4kCkUqybTavGUIl7igV1tMvwvJYUC2duQwqleBAnKzUC7RMyp7hTmukT1teSooiNZPOxT/DXJRI/eCtn/5ziLtgniOgTRHQXEb074OcTRPRfRHQ/Ef2fqPUt2oXhDedtjLWRzfSJfNkn1lU0TI1V25RixhhOL9RalOLxIXET7UyGlpxirQsB6qIwXNskarjSOxHDiyLSU2w2499UhTBUUtuVYmc0Idm6y5r0FEvikdY+QQOqFDcMsy1OE5A+1TQYnnOxpJL4SDbXIePPNIP4UCeJh19RXFYJhOT318jbOBG9DoDKGLsewB4iusBnsTcB+DRj7BoAo0R0Tdg651cb2Dk5jMu2RfuJgWw9xe5JBX7s2TSCgx6leKmmY7VhOBnFADBa1UAEzK/UvatIDPPk9OZZKXZvU0+VYlHpE0brUN5IRW3JXra2p8P0Ccc+ISUQSThONGTH9olBTZ8Isk8M5v4QgTt9ArCLYpGRbKz1POejI/IhRhIET5hwF8VEhIqmOAVzXOJoW3sB3GR//3UAL/JZ5iyAy4loHMAOAEfCVrhU0/HKy6diezA7nUUogrCcYsDyFR+YXsJyTXeU0I995yAA4PzN65zlFIUwVi2JsU940idKXegqJArDZT8Q2+Y5+Oea0rS9pMUwTaiquyjWsOKdaBcS2xdGlqkqkmJhdjgawRlUZTTIPiHbPHeOM9GOxCvFfmlPjqdYageSAJpKcetnvaJR4qZvcdo8jwA4Zn8/A+Bqn2XuBPAqAL8O4Al7uRaI6B0A3gEA5anz8cortsbeyCyjq6KSBfZsGsHimo4r/uRreO1V5+CybevxwduewRuu2YEXX7S5Zdmhkoq1hojmHa3ewrwrxSXV8vgK7WgXUhWLnESjm61K8XBZ81GKra9Jh7abbZ7l1V4SDrdGdawUK4NZBFo5xe0Xb1UZzIcEETDPA1pZVYTde3jh676/8XNe2ickQfjZJwArgaKW8P4apyheAjBkf78O/uryHwP4ZcbYAhH9NoCfB/BR9wKMsY/y10a3X8Su3L4+9kZmOcwcNTR+4wWbcMnWMeyYGMK/P3gM//7gMbz80i34s9de3qaEixqyMxlrOQhOUZzD4sowrZvSWsMUmlMcpspaHe26k4k8UvbxFDvpE8nWzc/rmlSKJRF4fZxJUTCYubyBSjGkfaJT+H7je1VTxCnFhp9SLHikUdJ/8Mnq3qLYsk+IV4ofgGWZuBvAlQCe8llmAsAVRHQ3gOsAfDNshRduGU0UX8X/0KQVvwjCJtoBlkUZ1ZPxAAAgAElEQVTiK79xIwDgU999FjMrDfzGD1/gu7yikJBhfeZVip0A9dSrFo5uMkcRFdd6OTynWKRf0PIUNz9owxWtbbIkV046Tp/I44GT5AorhjB57B9HUQbTkxne5jmDDeoDTMZAaJ6LZYGeYtPnWioj2SRR1Hw8xfz/3SiKbwZwBxFtA/BKAG8kovcyxtxJFH8J4JMAzgVwF4DPhK0w6XU9y+YUYW2evbz1B3eH/lxUD3eDsZaiMM/2CcNkTvHXK/uEqP0MtHqiAUspPjHX2to7LMs6DJ6qksemK5J8EXXORzGoHdwC2zwrcji+U0zPnBZNJWEWML/uoI59QmoHkgCCPcXJJ9pFFsW2JWIvgJcBeB9j7CSAhz3L3AvgskTvnACFCCWFMmlykDYKyY2o/FzrotTcnpLCi6v8XTV0k6FkP72Jmvzm/fu9qAoJm5She4ri4bLW1ubZO/EkLrLNsyQuUQ1rolAIYLBGNTpVm4tIYE4xpFLcKV77WllV2rLb06wbaJ1QKpViSRSBnuISYbUu3lMMxtgsmgkUmVBSKZMmB1HpE0lQBE3uMBlrzSnOs1JsuJViMev0tgH1ogpsVNCmFFdULNeD0ieSrVtTCCoh8ZOsZPDwnodJcRogsHDrUT+hmwwmg+9EO0UBGPJ3vSwCrC0nn4Tde7hopMlINkkCeIOOito+0S5pF+HM2jwnpawp2TTv6DCD1g9RSjHz5PQ6nuIcKo66yZzmIqIKVdNESyKEF2uinZC3gm6abekTKzX/nOJOipaypkj7hCQSw5NNnhQaQLWNj5z5d7QTd40YNLwjdWWVhN2bnVG3lvQJ66s8XpIguG+4Wmr3FBeizXMnVFTKRFFz2jwLUopFfLC9OcW5VopNEyWV7Laq4jzFYQ8pIjNZ/TzFdcNsmRyXxHfuJasREEmxME3WcYtnoHm9EJXKUgT4w2ZQ+sTg7AmxeEfqSgKVYv+cYqkUS8IJ8xSvJby/FqYotpTi7NInBNTEUAXNAPd6ulTFameYx6KYe3IVQSo5wHOag3+uCpxE480pHqlYjqNVl6+4U08xYA3tZuGVlxQLr7c9KfzcHKS6gqtH/vYJmVPcKe1zWsSNdvHV+He0C//d/dMrePtNT2F6KX2DLEmxqAXYJ/paKS4L7q8eF7PDZAE/RCmYfh3dRLfaFIVhF5XWTSj9+hhjti8yxD5B4iba+XmKAbT4itN0GytLpVgSA29edlIGcbJSuH1C5t52CvPMaRGqFJvt11LHPhFx7t5/ZBGPn1zBJ+89IWRbJMWhppsgtH/Wq5ri+I3jUpiiuJSRoubkFAvwFItSSxna7QOaQrn1FFtKsZgbclRuNP+ZyIl27pziobKlFK/4FMWdnCNlNRuvvKRYGGY6TzG/XgxSDBn/XPlGstFgqeYi8YoSpW54iltyim2lOOLeeWSuBgD48uNncXh2Tcj2SIpBTWeoaEpbsk5Fs87NJNbNwhTFFY2yad4hMpJN0JCdYbZvj8gZwCLhRaWl3orJaAbC7SxiJ9qxFtWi2V2x+bc0O9p1MtGOZPMOSSR+n/kk8F9lA3SqcaXY1z4hcN7BoOFNPyoJHMX17WjnjHKE/+7RuRp2jlcAAm7Zd1bI9kiKQU032/zEgKUUmwyJRmMLUxRn5b1sxm3lJ33CG54O2EpxDoviFk+xIOsIEH48eCarkCLcoxTz73WXP4P/WR2lT0ilWBIDk7GO7DmcQVSKQyfaSftEx3jvPyVFEW6fUD1zZoDoc/foXA2XTg3jiql1uOfQopDtkRSDNd1syygGmrnFa42+LIr7IacYQryupk8Af16LYsOONFMUMWH5vBj1EX8c4l5E471fq5eTNyJxN0pJMxlTeoolcUhvn7C+DpI6GmafUKVS3DHMO9FOJeimIBHCJ5LNOXdDLpM13cSppQa2r6/gunNH8fSZVcyu6MG/IOkrakFFcYkXxfGbyxSnKM4ozzXOcH1cRHld/QL4NSWbiYhR6EbTUyxEJecPKRFKMSDm/QxPTnGze2Bz3c0YoQ7tEzk8bpJ8YbC0kWzxfJn9RHOiXfttTirFnWN4Itn4Q0dDgOLjJzDEiWQ7Nm/5ibePV3DduWMAgPuPLafeHkkxqOkMVb+iWO3joriUYU6xQp35Rb2ImmjnjWQDLE9xHjNIDZNBU0mcnzpGGggvYkXsD17UO+u2P2S6X1HcQdEyVFLb2kZLJF4MQ1TzDkEbVADCJ9rJNs+dYnW0a28eJWJuBD8/3UJEc+Qv+Pf4JLvt4xVcuGkI40Ma7j8qi+JBoaabKPt5im2leLUfi+JKRt5LI2UUkhtRhaFfTm8pp0qxFWlmzQoVmj4RNtGOxDUzMRlzLvpA8wbgVkX423RStIxVVSysyaJYEk7a65AqPcUt8HkHohoKDRLe5h18IqOYojhkol3I9ZwrxTvGK1CIcMOuMdx9ZBk1XV5bB4G6YbZlFAPNZh6rCYSnwhTF1jBzBkpxRPe0JAjLKWYMCorhKebNL0RlBzvDayEFghP2LkIptot6TklpV4rTeIrHKhoWarq8OUtCMVM276AYhUW/UQ+xTzSH5Hu6SX2Bt3mHIxQIEGX8rGhR9olbHj+Lbzw1i/GqhlG7udJLL5jAct3Et5+aTr1NkvzTMJjvw28nD2zFKYozTJ8QpRRb9on06/FTivNaFPPmFwqJUamciLzQ5h3WVxH7w5rg1Px/SeM3AHf6ROf2ifVDKgwTWG3k79hJ8kNapXgQO9rxz3+QUgwM1sRDUbQrxeLsE34T2/kzjV/NPbPSwF/cehiH52rYe/565/VrdoxifVXFlx4+nnqbJPknqCjmryURVDVhW9Vlyhq1FCK9wjDFNO4A7DbPgiLZvNukqXlt3mG6OtqJmGgXrco224KK8hS3R7L5p090YJ+wlY2FmhzmkwRjmOlGrJzJpwNUBPKPqOZzseC70jAZSmoPN6oPsDzFzf/z/StiJNffPhF8PX/shOUb/uvXnocrtq5rbpNK+G+7R/GNJ06hrpso+0zCkvQPuic6lVNS20WsKApzppRVBQYTo/4lwUw569uNiPSJoKIw/0qxmOYd/G8MU800gZ5i3qaawz9krRPtrK+dPDyNVq078qIsiiUhpG7zLPBBsSiEdb8cROVcFF5LoVhPsfXVv6Nd+/KPnVyGphAu3DTc9rNzxkpYa5hYk77ivqdhMN+Jdn1unxA3RJMEQ7B9Im1hyItqbxpGSSU0clgUO55ihYT49+L4d53hNgHKuW4yqC0T7dqbd/BCgzr4NI1VpVIsiSZ1TrH9dZA8xWHXikFUzkXhbd6hCnzgaj7INF8LO1aPn1zBhZuGfDNqndSKHI6gSsTS8ESncriIlSS5rDhFsX3S9zqBwhA40U6IUux4altf15R82icMg6dPiLkBmTE8xSK7dwXlFNd9Itk6KVrWS6VYEgPTbJ9HkISmUixogzLAMBn+8CvPYv/0Srzl7c+l380yTvatxB/vRDu+e0Wl/VjrbI9k865eNxmeOLWCy6ZGfNclH3wGBz1wol1yMbU4RXFGSjHPKRaBiDbPTptjz0bl1T6h85xiIiEJC7zwD1PvHYVAQNxFW0c7J6fY7Sm2vnbkKbaV4sWa7GonCUY3zZQT7ayvecwyj8uZFR23Pj2H7x9birV82OeS7w8mP3aJYZ6Jds3rrQgRwvrqV3R7RzkeOb6ENd3E5Vv9i2KR2yXJNw2TOYKVG+4zTuJ3L1BRnJFSLNA+QQLtE22eYjWfRXGrpzj9+vwmYnhpFgAC3s/jKdZ8PcU8fSL5+kcrllIss4olYRgMLRM+k8LP4CIro8t16wMdN/rLSarx2W0iR5MGDdPTvEMV+MDld3/zO1b3Hl7A791yEBtHNLxgx6jvukRulyTfNIzWfgKcvlaKeQhzr7OKxdon0g9fBiUd5FcptuwHouwTYZNnOPxnuiClWPFRiluad6RIn6hoCqqaIu0TklBMTzRgUkT6PrNi2Q7gj1sU88+ln62p2eGvuPsjK7yRbCIVWf+Odq0/+8oTM/idLx3A1GgZH/upizA+5B+i5TSsyeF9USKWhsGcHgJuOkmfKEwkWykjpVhkTrEITzELUEpLipK7jnamyaz4OHuinQj7RJycYpFtnr3pE/x7UekTgOUrlkWxJIy0I1b90Oa5qRTHu8Hxj6hfepDqJBoUeIdkRLunWGBR7DM50uv//vD3juHiTcP469eej5FKcJ5eP1iGJNEwxqCbPW7eQUSfIKK7iOjdEct9iIheE/vdE5BZ+gQLVyWTICR9IkD9yKN9wj3RRRHgpwbcHe2ClxF1MeQfNvewtWqr3i05xU4iSGfvM1bVsCA9xZIQ0nbW7IeJZSuNhPaJkJbw/fCQkBWBSrFA0cP9IOONZFupWz7isILYvV15uy9KxBLWpEdVLOuY0KKYiF4HQGWMXQ9gDxFdELDcjQCmGGNfjv3uCcgqfULoRDsBSrHfRQOwCs+8PRE3rQ6K3bxD3DrDCgRRw3l+Q3lE1KbK84kn3pi8uIxWVRnJJgklrVIcNFmpSHClOO49wGCW5cTvc9kPDwlZ4W3e0fTuisspVv08y/axClIFvchjPBjwe7HfOUFEKKmEmuCJdnsB3GR//3UAL/J54xKAjwF4joh+zG8lRPQOIrqfiO6fnk7ej7zSQd6cCETnFItKn/Be5zWFcmef4H+rZrd5FtnRLuyaKGo4j3uSvcff6h7Y2tEujYo3VtGkfUISipGyiVCzQBC1Rb2He4rjKn9hn0s5tN45XvtEU4QQsW4f+4Qrko0xhrrBnGHxMPgieYwqlYhDd9UZfmgKCbdPjAA4Zn8/A2CLzzJvBrAPwPsAXEtE7/QuwBj7KGPsGsbYNZs2bYq9gZyhkrWp/MLYK0TnFItKn2izT+Rwop27+5xKYto8x+loJ0opNgI+bN59nbZgWT8kPcWScMy0zTv6oAhsKsXxbnB8PoMfTiRbcXdHZnjtE81zS4BS7BM56h7lcFp3S6VYYlN3lGL/crasii+KlwAM2d+vC/idqwB8lDF2EsC/AHhx7C2IyebRMgDg1GJD9KpDydtEu6A2zyXbUyxiMpsonKJSFegp9gl398Kvl2kfEoIK8JKqtHiKGQuPiIuCK8V5OnaSfOHNy04KtxAU+RxLHMkWYn2TBVPndFMpboo+zdecFAnGnAeicoyi2FGKC/wgKInGsU8EfNhLKiVKn4hTFD+ApmXiSgDP+SzzDIA99vfXADgUewtiMlJWMVpRcXKxLnrVoRhMZE6xf//2JPh1/AHEXphE4bYfKALi6ADXQ0HImStq4ocZsyhO24J3rKpCN3s/CiIpDmkfzr2+zCLCJ9rV9bie4mClmPpgf2QFY6zFvsfvRSIiMPk9oiXdwhXJFjVU7kZkKoYkv/DzLmj0oNQFpfhmAG8iog8A+CkAjxPRez3LfALAi4noOwB+FcD7Y29BAqZGy70vilP6Rd2IsBAYIUoxkK+nYndShojkDcCl3saZaJfSSxZ0AbY8xe5ItpSeYrur3dxKb89tSXGwJo2lV4pzdHlITNNTHDOSLeRBQukD5TwrTLRef/n1UYTq7nd/c6v6XBWM4ynuB8uQJJrmORFQFCuUqL9FZE4xY2yBiPYCeBmA99kWiYc9yywCeH3sd+2QqbEyjs7Vuv02LTCBkWxC7BMh6ROA1VSimpOeLO6WzKoixlMcpN66EdXz3p2e4aakKmi4LrSmmc5TnFXcoKQ4GKZ/3m5c+P1ioNInQhqeiOx6OWiYplcptr6KmNDW7ELoTp9ojoLyYx/HUyybdwwGvCgOnGjXBaUYjLFZxthNdkGcGVOjZZxarPf06T7t0LgbhQiMpVMnmpE1ra/7NZXIGrenmIggYtOC2ly7ETXRLlApVlrTJ8yUnuJm1538HDtJvjAZ821XHBfqAw9tUk+xGWJ9k57izvFe70R2S3Qm2rU0B+Hvy5xRgiSeYnmM+5uwnGLAUoqTpJblQ1KMydRoGSsNs6cz9a1kATHrElGsBbZ5zqF9QncprSqJGaqM1eaZxOwLw/B/rzZPcUrfOf/dJJMBJINF2ofzZmEhaIMyIPlEu2hPsSyYksPAPEWruHuP6SjFzdfckWz1CFXQjaj7gCTfNDJIn8gNU2NWAsWJhd55L02RnmIBE8B4UeiXUwzk6wLQmlMstqNduKfY+pp2qDjIwG/NZm2u25p40vk50kl/dslgkdai0w/+yuWGJYbEb/McnD7RbPMsZNMGCsP0KsXWVxHWHL90IdV17uodeIqLbBmSRMOvB0EPSt1In8gNU3YsWy8n24lMn/C2q+wE50naU4SVHLUxPxeA1vQJ0R3tgpcRphQHqNKaqrRM9kmr4uXxgUaSL/S0SrFS7IlljLHOPMVSKRaO1dGu3fMrRiluXSdgvRfBOlaJPMXyujoQ8Pk9YfaJJBPtClYUlwD0tigWqxRbX9MoxU5kjefIVew22L3u+BdGW0c7gcNrYaqZM9zWxUYpjZb0iXSeYk3aJyQRGIxBjVEIBMEvF0WNIFttGM61L5F9IuDa7c6+lSTDBPP1FIsYhQiK3OSRnnwuR1Ambcvv9MHoiCSaqIl23Yhkyw3jQxoqGuFkD+0TXVGKBdgnvIV61S6K12JmePaClo52gtInYkWyCVIu9BBPcctEu5RD23KinSSKtB3tih7JtrimO983Yg61hU1O5LuyqMp5lpim/0Q4IUUxF328OfxEdvMO2z6hxVeKZVHc3+gRkWxdSZ/IC0SE8SGttxPtzPYPaKc07RNplGJ/+0CllGelWLHTJ0RGsgUv4yjyKQ2D7vQMN15PcdqcYmeYTyrFkgDST+a0vhbVX7m4ZnUyHSkriTraBT1I9MPEw6wwPc07oubKnF2q4d8fPBpr3VYed/vrVs69OxEoQU6xfPDpa5r2iYCJdkofF8WApYiuNXpXPFidpMSsq5vpE45S3MN9E0VLTrEdR5eWoL/fjah8Snd6hhutLX0iXZZ1Hv3gkvzAGLNbiadQilHsCDKuFI8PafGLYhY8giO7nXUOg2eiHd+XAcfllkdO4Ldvehgn59ci1+1VoTkKtXqKY0WyOcc4P/dEiXj0CJ95Se1jTzFgF8U9VEOF2icEpE80J9q1vl61h5N6uW+icCutCom5AemxlGKxE+28XqWSSi3rNkNmucdBeoolYcSJIYyiOXpSzCKQF8UTQ6XYN7gwT7E7+1aSDO88GyVirkxNt0Z2Ty1EF8VBEaiKnXPvJA3EKIqd7ZKX1b6mHuEz72tPMQBUS70tioVOtBORPsHDzT0nQLWkAshXUdyePiFwol3IMRF1w3NvvxtN8fEUp4pkU1reTyJx49flKyncU1zUGtApioe12A2KjBBPcTONQ8jmDRTeicWKnQ4R9MDFBYTpxehutEGWF0WxrrNRLX3dSKV4MBjo9AnASlmo9dAiIFIpFpE+EdTRjSvFvdw3UXhzioXkWNp/XnhOcbeVYqXNUyykeUeOJklK8oNfl6+kOFmvBa0Cuad4fEiDweIp3mYMpbioynmWMLTnsqtKSFFsXytPxyiKzQCbkEKWqNJwrslxPMW8KI5cVFJg9Ij0ib6eaAdkYJ8Q3OYZSDnRLshTXOLpE/m5ArSkT5ConGKu3gYvE+Vxiwvffq8q7w0DN0ykat7h2CekoiHxQY9xzkdR9DbPq3bjjrGqNSIWx1ccJmgU3WOdJSZrt++FNWfi19HTizE8xQHqvkqw7RMJlGJBE64l+YY/KAU1dCmryWqP4hXFWdgnhCnF6Sd3BNkHKlr+imJ3+oSiiFGpjBiqWZTHLS5mgFKseTzFLGSYNg582CfusLBksOD3dO+EzyQUPW2Bp+qMlK2iOM5wqGEGe/35rpRFcXJMHxEgTCnmRakQpTiJp1hOphwImhP6/X8eJ9PaTfGKYk3paeyYFRGTx5zi9nWXVcpVUexWihUiIZmgQfYRNwqJmdjn3n43muJNn0jnKZYT7SRhNJvIdL4OEaNUWcJtYevsojiONSrM1iSiu+ig4m3eAVj7M+iYOPaJhRr+5EuP4x/ufDZw3UZA2pPlKe5MKZYd7fqbhsFQUihwtDYoqi0ITcRG9ZJqScFao3cnuWGGd09LgtNpTUD6hN8mVUu99VtHwRUC7ikW1fFIoWi7goii2K10uymp1KLqBqkbcZHNOyRhiEifKHraQt0woFAzejJOq2fDDN5n/NWi7o8s8YsHVCl4IjUvSo/NreL2p05DNxkMk+Ht/21P27JBme+8eUdU9zLv7/B1SvqXhmkGTrIDgifgBVFIpbin9omUQ+NumrNhO1+HYx/wuSj0et9E0ZJTrIjxFOsxPd6qgCI8SCkueXKKzZBh2jioUimWhBCntXkURR9KrjVMlFVyhs3jfFasa4X/z1QBAsWg4mdLUShYkeVJPU+eXIBuMoxWNfz97c/4LhttnwhXBd3wYy+V4v6mYbBQO02cByg3hSuKK5oC3WQ981+aAu0TIrJCmznF+S+K3TnFRGKGbuNmAiuKiPSJptLtRlOtc5DbQVKnT/CLtyyKJT44SnGqNs/W16LWgDXdRFlVnGHzOKMqYZ9Lvj9kvZQcBsB7KqpKcLoQvw7zc++qnROBI5pBPnDHPhGhCrb+TrEtQ5J48AelIOJYbdwUrijmw2e98hUbZnv8TKeI8BSH2ScqWm+tJVG0p0+ImGjnH+7uRYhSbAQoxZ7It7TnCBGhpJAzi1YicePMI0j14GUrxQWtiuu6VQxxf2Cs9IkQ+4SorpeDiJ/FIVwpbr6uKYSLtqwLzGQ3mf8xU91KcdyiWCrFA4FuhivF/W+f6HH0mNXmOT/pE2Ftjqul3k5CjKI1fYIEpU/EtE8o6Ytit9LtRuPNNoymApJ2NEFVgEaOjp0kP4hUiotqF6jpBsoqOQ+kcTzFYaNKRd8fWWK1Ym59LY5SDAC7N45gqGy16vabeB2oFLsi2eIXxeJGKCX5pWGwwDg2YCDSJ6w/sFdFcd7aPAelTwD5s0940yfE5BTHS3qwLqKCPMWe93MmxtlqR1Br0iR4W0dLJBx+HseJoQqi2U2zmOeYZZ8g16TUeJFswekT1ldZEyfHSp/wTrQLUYpdqvBFU6NtI20t6w6YaMebP1lFcfyLLZ+gJ+lfGgYL9Q33vVLc6zxe66lYsH0ixY2Jf779hlIt+0R+iuLW9AkxN2QjpqdYJUrdvMPxb/tMtAOaym7QhTwJKiVrRSkZHIIa9iSh6B5abp8oa/E9xWFRiUWfeJgljLV7ipWQ4lM3m+ruRVtG20ba3BjMP29WVaxzt2GaiZQ/VZFiQ7+jD3z6hG2f6FX0mNGF9Ik0n9GwzNJqiXJln2jxFCuCPMVGPOVexES7ZvvI1hOAK3Z8/WZM9ToMTSE50U7iixHwcJaEokeyNZXiZJ7iIAWp6PsjKxhjdkc7j1KsBHcQ1Q0TuzaM4NdefD5+/Opz2kba3JgB9jilA0+xtV3Btg5JfxA10a4r9gki+gQR3UVE745YbgsRfT/RFiSk2mOlWGibZwHpE/x3/SZ25c0+YbgyJUmUfSKBUpz2hud4OT0X4ZLCb8xcKU5XsAB2lzyZUyzxIWweQVyIrMbGRS0QLE+x4vIUx7BPsOBINr4vZU2cDL67kijFhmlZHt71iouwfWLYebDxu96ZzH8UlNvvOimKpVLc30RFsglXionodQBUxtj1APYQ0QUhi78fwFCiLUhIL4tiZ9hS1ES7LqdP5K0o9qZPAOlvykFKgpew2dBx4b/v1+YZaF7Uw9rJxkVT4t3oJYNHs81zupOMqNj2iVZPcYyJdiGNl/jL0m+aDMe+5+MpDhJ7vEVL8/rZfr0LEj1UBU7zjkSeYqkU9z0NM/xBqRv2ib0AbrK//zqAF/ktREQvAbAM4GTAz99BRPcT0f3T09OJNtJNhadP9MA+0bQq5Cd9gn/A/bapUsqbp9iyOpDddhlIP1wZ184i4mLIPdGBnmJDnKfYsk/Ii7eknaZ9It16ijzpqOaNZIvx2TZCMuZJgEAxiJhOUdz6uhKS9mOYrROhnJG2gIl2gfYJM3qo3IsmleK+J+pBqRv2iREAx+zvZwBs8S5ARGUAfwjg94NWwhj7KGPsGsbYNZs2bUq0kW56mVMsIh/UjZD0CWeiXfvPqpqCusFyc6HXXbO/RfztfJ1xClBrNnS6cyQyfcI+GMKK4pTbK+lPRNgnAK4U5+PakJT29Ik4nuLgB2jnIV0WTIng509b845QpdhsmZfhdCX0uYcHTWxX7HO3YcRv3mH9npi5LJL8okdMvuyGUryEpiViXcDv/D6ADzHG5hK9ewc07RPdP9GD0gc6RYSFwLF0wN9TDPSusUkUhmk6CoEoD1/clsphykVcrKYc7Q9F/ALPi1ghnmKFYmWvSgYPx9ue8hwTlQCTBdw+wbtTxfUUR6VPFHR3ZEZTKW7dr0pIsyTD9NonWq+fLcsGxFtyz3LUULkXOQLX/0T5zLuhFD+ApmXiSgDP+SzzUgD/nYhuB/B8Ivp4oq1IgFMU98I+ISA0342Q5h3cUxygFAO92TdxaFGKuYdPQKEaO5JNwHv5zV7XvEqxXTynQaZPSIIQVxSLmeyaBTXdsO0T8ZRixphMn+gCTU9x6+uqEqIUe/KieZHidwz9ki34+psT7eL7iEQ1jZLkF9E5xVqMZW4GcAcRbQPwSgBvJKL3MsacJArG2H/j3xPR7YyxX0y0FQnoZU4xf5AVZZ8Q0UUpbCjV8Vv3QEWPg7uo5BdFEYkQsSLZBEy0C3qv5uzppqdYhFIcpyGBZPAwBc1tUEKGuPNOrWHa6RPxItmCvK8cmVPcGc2J3j5KcWD6hNlSyIbmFAd2tHM370imFMtj3N9EKsWii2LG2AIR7QXwMgDvY4ydBPBwyPJ7E21BQjSVoCm9yeMNywTuhGZh2Pk6WMgNMm/2CUsptrbJmdiSctPChkTdiMhF1k3WllEMoC0rNaPl2cQAACAASURBVO42haGp8XySksFDlFJMBN/WukWgZntJVQUgRHe0i7K+8Y9rQXdHZvB7V5unWAme/Kh7suWdkTa/nGLGIiLZEnqKZVHc9zTMiIl2XVCKwRibRTOBInN6FT0m6mbEUQWoE/xe4FeD9TrDOQrDNazBz0sRSnE8+4S/EiHivbwXdRFdDzUirMmJdhIfmpapdOeYWlD7BGPM8RQTWRaKqAdIfp0MunY712JZFSeCIVgpDvKruzvaAUA5VCn2F6GcSDYzefqELIr7Gz3CPqEQhf68bXkRG9VrqiXqiW/WFHQz4igCLATODdKvKO5hXF0cupE+Edc+oQq4GNZ0E2VNbXudD+HqLekTqd7Ksk/kxPYiyRdhMYxJICpmEchHvnhhVVaVyEi2sOskIMbKNog4lsK29Ing6DPdMJ0RQ6Dp8/abQxFkRWuJZEviKRYwt0SSbxqm6UzADaKsJThn0m5QFlR6rBSnVQE5IpRinr7g19Gul37rOBim6aiqzdneAoriOOkTAgqAum46+9SNN3xeiKdYJd/hRIlEZPpEEe0TPGmC3/i0WEpx+D7jLxdwd2QKv0L5Ne8IVYpb7BNhOcVRkWwJPcWqLIr7HT2iox0AfOhnr469vkIWxVVN6YlvVtQEF46Q5h0hqmRVs36QL0+xpyhOuWlxM4FFpE/UdMO3KOZKBb9ZG6b/Q0oS5EQ7SRBBk5uSUlTVrNbwKsUUGcnG/04tIpKtiPsjS/hDVVub55Ccda+n2EkQ8blPBXe0syPZEnqKi9ywRhKNYTIYLDp2be9Fm2Ovs7BFcU/sE4LTJ0TZJ4IKsLzZJ1rTJ6zXxKRPRC8XFhEUl7pu+g67lByl2Fo/i9llLwyZpykJQhekFBe1zXNNNwA0vahxPMVO+oSMZBMK369eoUgNObd0kznqMNCe896yftP/POdpQnEKoJbtkp7ivsZ5+BWVhoCCFsWVUo/sE4Laq3Ka9onO12GG2AdyN9HOJ31CTE5xb5TiuuFfFHvD54WkTygyfULij9Cc4gIWCHzki9snSooS3z4R6CkmEIr5kJAlwekTwUqxu4kT0N4RtHX9wZFsNXvORRJPsSyK+5u6fWxLfo0bOqSQRXGv7BOiPcUi1AkjJOkgf55id/qE9TWtMBM0vOZFUdLnFFsz3n2UYk/4vBmzUA9DlfYJSQCiOmtyX2bRqHsm2llKcYR9IsYkaQrxwUr8MQMmMFrdEv1/x+v5jOxo59e8g6htwmUclJAJgJLiwyenl7UBV4ot+0T3T3TRbZ5F2CfCPMVDtn1iNSf2idb0Ceu19OkT8R5SVAGqWE03nYYobrS25h3pH5xKsqOdJAAnXkxE844C1gdepdjyFMeMZAvZZ0V9SMiSZkc7r30ixFPs6QwaqhSb/sdMUdpTSOKgqcUcHZHEg18HKqKG81HUorhX9gnRbZ5FpE+w4JbCJVXBSFnB7Ire8fpF4laKxaVPmLHsLCI62gUqxd42zwI8xapCkTFTksGE39TTjhAqSN/QJgtqDe4p5kpxDPtEDOtbWBc2iT9BnQIVJdgWqJtmi6e4FJZTzJjvee5uUZ7EUyyPcX/D75lJG3SEUciiuKIpWLUvlN3EsU8IVorTNe9goUX65HAJMyuNjtcvEt00fdIneuQpFuAlC55oxyOFePpEevtEnCFhyWBiiLJPKMWOZOM3vooW3dE0TrazFVEnaCMHBP5Q5Z3sbc3hiKcUOznFARPt/O0Tze9lm2cJh1urkuQQR1HIonjHeAXzawZOLta7+j7dimTrln0CACaHtXwpxSpPn+B/e7p1mixe221xE+3am3fwizr3MzGW/sFJU6z1yAu4xIuoEStCMc8vHsnGR23ijBRyETLsQUJ6ipPD95b3GqyQ/7llmAyMNRMngKb9rB4QyeZ3fVda7Bdyop3Egk+0i2rekYRCFsUv2DEKALj/8GJX36d7bZ47X0dUS+HJ4RLO5kYpbqZP8F2Y9gLlVp/DEDHRrtbwzynWVKVlYlzcyX9h8L9JqsUSL6JGrNxD0EXC6ymuxIjkjHPtlkPryeEPEW1KcUDxydVg90Q7J9LSt3lHUEe75veJcoplUdzXcBvVwBfFezZUsWFYw31HulsUi2/z3LreTjBCPMWApRTP5EkpFuwpth4KopdTKb1/MiiSDbBUK56farJwS0scSrIolgTgZHGKSJ8oYIFQN6zPGS+G4qQPRbV55j+TNXEymh3tWl8P6iDKfcOt9onWicot6w+YtOy+vsqiWMLhE+2SjB5EUciimIhwzY5R3HdkEQ8fX8JSrTv+YlGzvjmi2jxHeYoXa4bv0FSvcXcyEtnmOY5/VyH/i24SagET7QArK7umm2DMGh5M29GO7yfZwEPiRdTDOQl4UMyCpn3CLopLipNZG4Rz7Y5SimXBlAh++nj3arBS3K7Yh6VPGGbwRDvn9xM171DkMe5jHKV40CPZAODanaOYW9XxK194Gp9/dLYr79EcthSzPhGFYdDsXM7ksAYAmF3NXi1u7WgnxlNsxEx6EDXRzs8+AVhDuHXdbHZ4SlmwSKVYEoQoT3G/RLJVtWhPcXM+SPAyhPQP6YNG0KTPIE+x7kySbF5Hicjq4Ok30Y4FR7Jxto5VYm+vGqBgS/oDGcnmYu/54/i5H9iMoZKChS4pxaIn2jk5xaki2cKHBDcMlwAgF75it/+X78JedbQrq9Ez1MNgjFk5xUH2CXsIt9ngpeO3AuDyFEtVQ+JBWPoEFTR9Qm+daFfRFOgmCx1Viecplh3tkuIoxZ7dqtp+de/5FXQcNNW/rX3QRHJ+Dx4qKdi2vhx7e1VFkaNvfUzDsU9IpRhDJRW/+oPnYKyids0qIHqiHV9XmidX02RQ2gavmjhKcQ58xQ2jXSlOe1PWDTNWAVrRyL5xdnZuNIdlgpRiFTXdEDa0zd+mkQPbiyRfODnFqZXiYtoFuHffHclmvR78WYk70a6IHusscZp3eO5BXKjznl9BObJ+rboNkwV6ivlh3DVZTfQ5UBU5GtDP1CPu051Q2KKYUykpqHXpSZAXr2n9om6sqLDOfz/Ic8WZHLGV4uXsleK5lTrGh62nekWAn1o3TCzWdIxV2mPSvHBVqdMmLzwbNbgo5vYJMQVLWHanZLCJ44+NQ1E7uNV0E0TNB8dqjHb2/JYQ9rmkgu6PLGmKAK2vO9d3r1Js8IeT1l/QfHLZHz+1CgA4b+NQ2/ty0WH3ZDXR9qqKIts89zHOfVoqxU0qavSki04xu6AUKymfXIN6w3MmhiyleCZjT3HDMLGwpmNypLUoTnN9mlmpgzFgfChOUWy931qHTV68Q7ZeKrZ9wvEUCyqKozp1SQaPOEkKcShqJBv39nNxolqKURQ71+7g9Ur7RHLMgIcNXpO0K8X+rZk1VWkTAO46vISSQrh252jb+/KRz+RFcTETVyTxaEaySaXYoaIpztOCaEQVPG7SNpVgEZm4FU3BaEXFTMZK8eyy1VhlwimKrdfTPBBML9YAAJN24R8GH2LttCjmQ7aVkn8BXtYU1BpNT3HaU6Q5I1sqxZJWDNOyDKUdsSpqswpvCgxXimPZJ0I72hUzjSNL+Onjlz4BtBfFQTaWkkJtAsBdh5dw1fZ1GCm3X3OfnbFU5N0bkhXFmlSK+5q69BS3U9EIa11SikWnT1jrSlcUWxPNwpeZHNZwJuOi+KxdFG+wi2IR3fzOLNmFdiylOPrGGUa0Umx5ipmgSVCqVIolARhma0ewTimufcJoeTitxLBPxEmFKer+yBIG/zkUQfY4/pDvPX81VWmZ73FweglH5xt40e71vu976ZYRAMBFm4YTba/0jfc33WjeES25ASCiTwC4FMB/Msbe6/Pz9QA+C0AFsAzgDYyx7vZgtqloChZWu1MAmoIKHjeqkk6dMAImIrjZMV7Fodlax+8hghm7KOb2CRLgKXaU4uHuK8VRPdUrbekTYiLZ0mYrS/oPMyKGMS4KEeoFrA+8KTCOUhzS1a6pFAevt6gTD7OEOx68t8SgiXZBjWdKKrUk7Tx6bB4AcNU563zf9xev24qfeN5GbLDnzMRFU0kqxX1M3WAoKSR03lfkpZaIXgdAZYxdD2APEV3gs9jPAvgAY+zlAE4C+BFhWxhBReviRDtB+aBu0g7ZmTGU4j0bqjg8t5ZpA4+ZAKU4jTBzZskqiidi2CeciXYR7WCDqEUUxWVPTnHa9Al+U5FKscSLEdGwJy5U0Ei2mt7aWTKOUmzESIWx9oegjRwQgjvaBSnFdlHsTZ/wKMUrdUu8GA2YRK2phE3r4kexubdL5hT3Lw2TCW3cAcSzT+wFcJP9/dcBvMi7AGPsQ4yxb9j/3QTgtJCti0FFI9S7NdFOcJtngKsTnf++GTHRDrCKYsMEjsxlpxZ7lWK+C9MqxcNlFUOl6NPWiW3qVCm2D1Jw8w7VnmgnZhKUM9FOpk9IPFiJM+mvQWpAg4W8U2t4PMXORLuwnGLra7inWNonksIfqsgbycav7wE5xe32idac4uWaNZFuqCzW0anJNs99TV03hbZ4BuIVxSMAjtnfzwDYErQgEV0PYIIxdrfPz95BRPcT0f3T09MdbawfllLc5ZxikRPtUs6GjeMpPm+DFWlz4Oxqx++TlrPLdRChLZItnae4ho3r4nUzctIn9A4n2jUi7BMlpSWnWFj6hMwplngwGRNi4aKCpk+s1HWMVJqjQ04kW5h9Iob1TdonktMcGWt9XXHsX637k6vBXqVYU1onyHOleEiLni+SBD6Hp4gjJJJoGiZDRaCfGIhXFC8B4MGB64J+h4gmAfwtgLf5/Zwx9lHG2DWMsWs2bdrUybb6Ynk7u2yfEOkpTjmcE0cp3jlRgaoAB8+udfw+aZlZrmF8qOTsOxGRbNOLNWwajVcUV5xItnQ5xYEd7VTBnmInfUJevHvF3Eodv/9vj+CKP/4aHjg0i+nFGh6zvY15QpR9Qilo+sRyrbUo5p/JMDHEjOEpJhnJlpioSDav6KGHeIpblOK6jpJKbcVzWlQB9x1JfqkbLBOl+AE0LRNXAnjOuwARlQF8HsD/YIwdErZ1Maio3Yxk64J9Qkk3GzaOUlxSFewcr+JghkrxzHLdsU4AotInatgY01dWdmKb0uYU+ysXllJsNjs8pTxHuN1jtUO7hySaJ04s4Cc//D0cn1sFYwy/+4VH8G8PHkXdMPHpuw/hXZ9/GD/zsbtzVziKsk8U1S6wVNMx6laKS9waFd28I0zQUAu6P7KkaZ9ohRfJ3kltPItY8xQuVlSaSymuGRgS2JXMeR81/QRvSX5p6Nl4im8G8CYi+gCAnwLwOBF5Eyh+AcDVAP6AiG4nojcI3coQrHa+3Tnp4/jSkpK6zTOLFxG3Z0MVBzJUis8u1bFhpKnqisopjq0UaymVYrsorgT4lyua1V5cd5Tijt7GYdh+H+6tk4jnjqencf+hWfz2TQ/h3x48hq/vO4XfeflFeN3V5+CWR0/g2/unsbCm4+CZpaw3tQXDZG1KWycUddLRcs3AiGsCVpyOdnEaL5HMKU5MUNQdr3m9D5RcDfaev1ZHu1aleKgktrgBxNj2JPmlbjKhjTuAGEUxY2wB1mS7uwG8mDH2MGPs3Z5lPswYm2CM7bX/fU7oVobgzETugsLWnMEsbp1pm3eYjLX1nfdj12QVJxbqmSVQzCzXMeGKz+FKV6d/e8MwMbvSSOApTndecIU5rKOde7m0FhuukizX+7cofvfNj+Lug2cze38+OejugzN41+cfxlU7x/GLL9qNn7h6O+p2K2EAeOhIviwUUV0s41LUtAWvfUJTCCqFF8V6jAmwBDmsnhSneUdA+oRXKXYm2nlsEWXVRymOMYE6KbwYl7Fs/UnDYEIzioGYzTsYY7OMsZsYYyeFvrsAql0sipu+NHE7nVIO2cWxTwBw8hznMmr3PLtSx2SLUpwuku2s3bij10pxWE4x0JwgkjYnsaQSVIWwUutP+8Raw8C/3H0Ytz3Zs2CaNhZtFf6ll2zG//uKi/CZt78QmqrgB86dwGXbxvDmF56LkbKKR47OZbaNfpimmIl2CoqnmDHGsFTXsc5VFBMRKpoSPtEuhlKsFtRjnSWOpdDzelBOcSPAU9yWPlHXnXu5SNKKMZJ8UzfE2ydiNe/IM7w46YYXsysT7RRCmtQtw2RQYgwz8SzfmVUd6/zz0LuGaTLMrjScjGIgfSQbzyi2lOLoZi1O+kTKSLaoonjNLorTPjgREYbLat8qxXMr1jFbXMvu71tas4qrj7/lBS2vExFueac1beLJk4t4+GjelGIx16C03TSzYKVugDHYSnFz23nznCCcYf6Qz6W0TySH7y2vx53v5/bmHcEd7Rqe9IluKsVFO+8l8WgYJsbUZA1doih8m+dySkUwjK7lFKdOn4hebnLYOlFmV3rf7vnMcg2GyVom2qX1dh2fsyYNTo1VYy2vEKGsKh1Hsjme4pCcYqD5MCbiFFlX0frWUzy3ain9Sxn+fUu1Rovi6IbI6or0/B3jeOL4QqaNb7zEadgTBwXFs0/wz8OI57hVS+GpQ01BI3jdSkFzm7OEK+uBzTs8Jxj3DXsf6kqKx1Nc07tSFEuluL+pG9lEsuWarnqKBcVtuVFTpk+YLF4B5ijFK70tQr77zBm8+K9uBwDsmGz2qecXp06L4memrclPezaNxP6dSkkJnaEeRpyOdoCrKBZQtVhKcX/aJ2aXrYezpbXeP6RxFtd0rKuGD449b/s46oaJBw/P9mirojFE2ScKmMvLH6LWeTqdVTUlvKNdjFE+hahwDwlZw/d4YPOOAE+xNzZL83S0W20YGBI8DA5IpbjfaWQUyZZrvBOeROIEwOcpfcKMN+lmcti6+c/22FP8ye8+h5GKhs+8/YV46SWbndfT5kU+c3oJU2NVjFbjD5VUS2rH54VTFEdMtOOeYhEPTiMVDSv9qhSvWErxcoae6aWajtGIoviHLtqEieESPnT7gR5tVTTTSzWMDyVvcesl7XyGLODny7pK6+e+ElEUB+Xpuini/sgavru8l0U1oPjkhW+bUqyS4zcGrOPcDaVYDVCwJf1BNzzFfVMUd8U+wZVigXsprVpjxLRPDJUUVDTCTA/tE2sNA3c+M40fuXwK15+3oWXyWVpP8YHTSzhvc3yVGLCGWNNMtCurSuAEOh7VxkcoRDysjpS1TIvGbjK3anuKMyz6F9f0QPsEZ11Fw6/sPQ/f2T+Ne5+d6dGWBWOaDE+dXMTFW0dTr6uIOcVLjn2iXSkOGwXSTRb5mVRIFktJ4eeP97oYdH3XHaW4vaOd3uIp7o59winWZVOkvsRKn5BKcQvNlIFu2Cesr6KV4vTpE9HbQ0SYHC5htof2ibsOnMVaw8QPX9LeCZzbCzppt8kYw4HpZZy/KdmMwaqmdj7RTjcD/cSAy1MsKH0CsG78/TrRbnaFe4qzs0/EUYoB4E0v3IWypuCbT5zqwVaFc2xuFUs1HZdsHUu9LqWAbZ6XHftE63GraBShFEd3ASzi/sgaR4H3vB6sFAd4ilXF+ZlpMqzUja6kTzjbJR9++pJ6VpFseaabSvH+04vYuK4svs1ziisxi+kpBixfcS/tE7c+eQojZRUv3DPZ9jMlYHayH19//CRe9cE78I19VlFyaqGGpZqO8zcnK4orJSVVTnGQnxho9xSLeHAaLmuOHaPf4OkTSxmmTyyuNTBaibbfDJVVbBgpY2a53oOtCmffiQUAwMVTYpTionkr+UOi30S7cE9xdGKHldtcrP2RNXx3JVeKW6+lln3COn78GtpVpThN5JMkt1ieYlkUt1BJ2aQhiLWGgdufPI2XXbpFiArIIUL6SLaY2zM5rPVUKd53fAHP2z7uqKhukniKv/rYSTx+fAFv/6f78fn7j+CZ09Yku/MSFsWWUpzCPhGqFNtFsVBPsZppOkM3mVtppk9kVYgsxZhoxxkfLjvbnCVPnlgEEXDhFhFFcfEiyHiEX7tSHB7JZsRQitUCPiRkjTPPJqWn2J1TzB98ulsUC1+1JGMYY2hk0dEu7zhKseCJdt87cAbLdQOvuGxK6HpT2ydieooBYGKohNnV3g1Xn5xfw7bxId+fEW8DGuNv33diATdesBHX7Z7Ee768D9/YZ/WMSWyfKKmdR7IZUUWxJ5JNkKe4Xyfa8WjAhsFCi5luYZgMy3Uj0lPMmRguZRJn6OXJkws4d3K4TSnthCJ2tAuMZIvKKTZZ5GeSpH0iMY5S7Hmd35O8neP4/9uadygKdJOBMeY0LOpG+gQvinWpFPcdzYQoqRS3kLZzWRBfe+wURisabjhvo9D1ikmfiLfshK0U90IdMkyGU4s1bBv3zxFuKsXh21LTDTxzeglXnLMe73/9lQCAf7zrECaGS7G72XGqKSLZojzF5S4oxcMVDSsNoy+7bM27Csws1HD+nnE8xQAwMVx2fNBZ8sSJBSF+YqCg9gn7uA2XPBPtSgpWwzrasWhLkyI72iWGX76917ug67tumlAVahtt5UPeDYN1Vynm2yVr4r7DabAlWCnum452ou0T9x2awfXnbQhVCztBoc5zilfrBmZX6hgfijeUOjGswWDAYq37V4TpRathx9R6/6K46SkOX8/Tp5agmwyXbhvDjslhfOU3bsRjx+axY3I4sY2lkkIprsW1TzjpEwLsE2UVjFnrFKEM5gl3gbm0ptudCXtH0qJ4fLjk+KCzYmGtgUMzK3jd1duFrK+I9omlmqXue3PAJ4c0LNdNrDVMVH2KqTjZzkVM48gaE/6JTGFKsVclBqycYuvnpjOPwu84pkVVpVLcr3DBS06081BWrRhx0UXx6YUazpnwtwKkIY1SvO/EAkwGXLAxXkHBu9rN9WCy3Yl5q+Pc1qCiOKZ94gl7YhFXx3ZMDuOVV2zF5eesT7xNVU1NpRSHPYG2e4o7epsWeCHcjwkUsysNpxDORCl2vKnxcq4nbE9xlkriw0fmwBhw1c5xIesrYhG4XNPb4tgAYMuoldt8aslfzbc8xeHrJhTvISFreG2peJt38OZMPukTvkWx4lKKaz1QiuVx7ju6pRQXvigmIiueR2BRvFLXsVTTEw/Xx8HKKe7sdx87Ng8AuHBjvFbHTle7HhTFJ+fXAABTY/4PEk6b54giY9+JBQyVVOzakCyT2I806RORE+1K3jbPYibaAXA8dv0CYwzzq3XsmLTOjcUMEih4FFwSpdhk2Wwr56HDcwCsLnsisJpVCFlVz1iq676jJk5RvBhQFMdRipXi7Y+scTratbV5tr56lWLDZI4q7IanUehGUyke6kIkGy++9R7lFD9+fB43f/8YTi2s9eT9Bpmafe+VnmIfymrnTRr8mF6sAQA2j8YrPpOgKp372B45Oo+N68rYOBzvxr5nQxWqAtx7ZLmj90vCCbsoDlKK46ZPPH58ARdNjQqxI6TJKa4Zpm+KBoc/nYosiofL1nHttwSK5bqBhsGwfcJq+53F37fAleIEnmIAmfqKv39kDudvXof1Q/G7OIaRNg4yC5Zr/g1XmkWxv8XFZNGWJgVSQUwKc9In4inFDcP0VYqdotjsrlLMbTe9yCluGCbe8U8P4Dc/9xBufN+38P0ctYrvR7hSLNs8+yBaKeZFcTeU4jT2iceOzeOKc9bH9tZODpdw4+5xfG3/Qleam7g5Mb+KaknB+LD/DZxvctjfPrtcx4OHZnHd7vac406IyjINo9YIzykuqQSipn1CjKfYuvn3W1bxrJ33u922Iy1naJ8YjZs+MWKdx1kVxYwxPHRkDs/fIUYlBpqfwSJl8y6t6c7nws2mkRIUClaKl2pGZH4pFfAhIWv47vLuWTVUKfbzFHP7hEspLnUvfaIXx/mLDx3HsblV/MlrLsWmdRX8xmcfwuJa9gk2/Yr0FIdQVsO7GyXltKMUiy+KqcPJLqt1A0+fXsQVCb21r71iAxZqBr762MnE75mEE/Nr2Lp+KLBgJyIoEWH5//XYCegmw2uu3CZkm6olFYbJ0OjArxIVyWbZdpr2DBFR1tw+0W+e4nk7FnCHrRRn0eqZq9NJcooBZDbZ7vDMCmaW68L8xED6VutZsFTzt09oKmHjSAknfYpi3WR45PgyLpsKt2CpBYmo+70vPIJ3fub7HV3HRON0tAtIn/CKHg2DQfPJxuMPLLo7faKbHe26fM4bJsOHb38GF0+N4i037MJfv/H5ODyzgs/dd6Sr7zvIOJFssihux12ciKCrSnGH6RN3PD0NkwFXJPQXXrNjFDvHy3jvf+7Dc2e6Z6M4Ob+GqbH/2955x8dVnHv/O2ebVtWWVdyLbNlyAxeasQGD7VDfhJjATYALN7wEcrm0F0hIJwQuCZdAbkzoceAGnAK+SRwwGGOMsZEt94otF0lWsSyr111tO/P+cXZXbSXtrlaWbc3389mPdkdnd+fM/s6cZ5555pmew020Xjwz/9xTzsT0BKaPjE0KqsBq5mjy4rq9enBjmO6wmrTYZp8ILLQ7x8InAvF1Y1P94RMDEKcb8NgkxYW/0A4GzlO88Wg1ABeMi82sCbSL6z8LDMEALW4viSEW2oERQtHeU1zR5ObnHx9nW0kjzW4fF43pOUtPtA6K08nmgmr+uqOU9/eW841XtzDnqU/YeKRqwOoTcGp0yT7hf+3rZLj7dD20p9j/Bo9Px+HyYdJEzHcmg9O30O5vu8ooqGrhwUXZCCG4cHwqWWkJbC6o6dfvHcy4g3mKVfhEF6ym2IZPVDa1YtIEqf4bYyyJJnyiqdXDz//5JRPTE7gsO7K8yZoQ/HzxSHy65Ftv5LGzuDai94eL4SnuxSjWQifL9+mSZz48xNaiWpbOGR2zHQTj/IvhItWGlJJmlxe7tfuYYjAW2zlimafYem4utNt0tBqbWWPuuKGYNRFc9HY6aW71IkTXfLfdMTQ+ED7R/3Vdd/AU963YGQzFAfj7rjImZyYyOTOyDWt6IiDR/jAQGpyefgnLWCmlDwAAGnxJREFUaHH5uvXuZyZZOsQUrz1cy9rDdTy9tgSB4RDoiTM9b7OuS371UT4jU+L494UTOXSykQanh88H0CjuPnwi4CnuWO7pZsFj5zzF8VZTTHeODdbrNCy0a/X4+M0nRzh/dArXzmjb7GvexGFsK6oN7uqniC0uf7pVtc1zCGxmEXXqrVBUNblIS7R2yY0ZC4w8xZG95+UNBVQ0tvLczecHDb1IGDvExjt3X4zZJPjGq1u48aVcdhbHbhGAy+vjVGNrtzmKA3ROCRW4iS7/opDXNxZyx7xx3HN5VszqFW0O67I6J/UOT6+bJrSfoYiFUZx4DqZkk1Ky7tApFkxKw241kRhnHhhPsctLorVrvtvuSI4zYlZPx1bPf8wr5sP9FXxv5V6klByvbmFXST1fnx27ASK09xTH1kDYV1bPrF+sZclvNrL4hc/5v29tj9lndxc+AYanuLLZHTyf3WXGdvD1rV6mZNhJsfccKqOd4dk4Pth/kn1lDTz6lSk8fk0OB5+8mhkjkzlY3thv39nbwEaXhkHcWZdteeg7eYp9EkuI8ImAp9irG57iUHHjsSC4ALAfPcUvfXaM8oZWHr8mp0O7zJs4jGaXl/3+rFHR4vHpvPTZMZ764GBfq3pOEfAU9zajGynnhlFs0mK6zXNlk6tfQifAyD4RiXfC5fXxl20lXD19OHPGDo36e6ePTGH1g5fx8KLJnKh38vTq2Fxgui75/sp9eHXJvInDejy2fehIQVUzV/56Aw/+eTe/XXeURTkZ/OJrM2K6krTNUxzZKGSXf9Vwb+1tNWt4/B6IWIyfAtknzqXwiaOVzZTVOVk0NRMwDP8BiSlu9Yadjg2MWY0Uu6XfwydaPT62FtYwaoidD/ad5M3c46zYWowQcOPs2MTWBwhcWb11PwdONHDV8xt4N8x4yE8OnkITgowkGwL4NL+SsjpHn+oKUNnYiturk9xNyMvwRCtun6Te6cXrk+w/2cJlWSnYLRrzJ/S+9kIIccYuOnR5fTz3cT5TRyRz4+xRgLHhxbSRyRyqaIy43o+9t5efrTrQ7f91XfLAn3fzrTfygp5Nt1fv4uWUMvSOqoFuu7NTNLCjXWfS/PfX5V8UsaukLqJrMxKCKdn6afSzp7SelzcUcNOc0Vw6qeMs7iVZxv1wS2HfQige+stunvv4MMu/KGJPaX2fPutcIhAWqTzFIbBGmX2isrGV+1bsZNHzG3grtyhYXtXk6pd0bBA6fGJ9/in+40+7eG9HaXBKIMCaAxXUOTzcevHYPn93cpyFhxZnc+/lWewuqefoqaY+fd4/dp9g/rPrWbWnnO9fM4XLstN7PF4TxrmX1Tn45ut51LS4+efecjw+yU9vmNanuoQikFItUm3sKq4j3mrqdeq6fcq2WMQUW80aFpOgpY/ZJ9xene+9t5frl23qMCUfKXmFNbyZWxR1CsFWj483c48DcFVOBmAYxafbU9zs8rKvrIHkCFObGVs992/4xLaiWlxenadunM7iqRk88+Eh3thUxNLZoxmREtvNg4Jxnz38nl+WN/Avr22hsKqF1zYWhGV8bTxazfmjU/jTdy7htX+dC8Cnhyr7XN8n3z+I1axx3cwRIf8fSMtWWu/icJUDh0fn6ilDee/Oadx5wfCQ72mPJgwv3JlkGNc0uyipcfDIu3sprXXyg2tzOvQtU0ckU+/wUBFBHtwDJxpYubOMd/KKKa4Jva7kpc+O8f7ecvIKa3l9UyFSSm5fvpUrntsQzI8PRp7iULNi3XmKvboMabTMGjOEhxdns2pPOWV1Tr539ZSwzycStH5caCel5IlVB8hIsvHEV7vev9ISbeQMT+LjAxVRa6y01sGH+yu4c944Em3mDnbK2YzT7SOvsKbbdjl0spFXNhT0eO/5YF858RaNYQmxSVkZIKzhmRBiOTANWC2lfDraY/qLOLNGdXMrDQ4PKd2kBAvF06sP8emhSrIzE/n5+wdpbPUyc3QKpxpbmTEy8h3UwqHzNs8vrD3MsvXHiLeaWL3vJMvWH+XWi8ZhM2ucbHCyet9Jxg2LZ/7EyGKJe+LG2aP41Uf5vLujlB9fH50xWljVzOP/u4+c4Un86Lqp3HBe6BtXezRNICX85+pDNLd6+ef98znV6MLl9TE+re+bdXSmbaFdZIbh7tJ6zh89JGTS+fbY2gX4xyJ8AgxvsSMCT+qBEw1MSEvosEjvu+/sZJN/odaL64/y/WtyIq5HvcPNfSt2UdviJq+whudvmRUyX2x35Fc08t23d3K8xsHSOaOCoTVJceaI8xQ3tnpwe/WwtoaWUvLX7aXUOz2k2C0U1zhYd+gURdUtvHTrnIi+19jquW+e4tJaB9XNLmaNGRIyFGLjkSqsJo1LsoZx/ughfPV3ueQMT+KXS2f26XtDEdiFrLsbkZSSn636ErvVxL1XTOSFT46wu7S+xxmTeoeb/WX1PHBVNgBZ6YlkpSWw7tAp7rx0fFT1LK938tt1R1m9/ySPLpnMhG76hpzMeOItGk+tLSY73RhAzBqVGNzJszcmDLWxqrWeZZ8e46HF2VHVNVY43T5eXH+UNzYV4vFJhIAfXZfDFZM7OhoCIV0HyxvDHjS9sqGARJsZt1fn9Y2FPLx4MjuO15KaYGV8WgLv5BXz4vpjfG3WSNxenf/+5CiVjS62FdWSaDNz0yubefX2uVyZk4Guy5CZdrrzFPe0icrDiyczJTOJ7MxEJmUkcezYsbDOJxLM/WgUf36kir1lDfxy6cxuZzPuvHQ8P/zbftYdqmTJNGO2rN7h5tDJJqxmjcmZiR0W/9a2uEmxW4JttnJnGULAPVdMRNME7+QVc82M4STYzCTazMzuw+xxKKSUlDe0UtfiZlJGIm9sLGRdfiWv3DaHkUO66q2yqZXqJjdTRySFHeq18UgVP/7HfkprnVx/3ggeXTIZp8dHUXULOcOTcbi9fPvN7dS0uEm0mbh0UhoJVnOH8MzcY9WsO1TJ3RemkdDL2p9I6fUuJ4RYCpiklPOEEH8QQmRLKY9Gekx/smhSMp8XNXHjy7lckpVKelIcQ+wWbBYNq0kL+WPVOwwv5QNXTeL+qybx7Te388InR4L/z0jur/AJgdPj470dpRRUtfDq5wXcPHc0T904g7zCGn71UT7PrskHjOwG00cl88iSyTGNb05LtHH19OEs/6KIZpeXyZlJ2C0mTH6jVZcS3f/3VGMr+080BNMB1TS7Ka11YLOYsJk13rjjAjJ6yToRQBOGmI9WNvPIkslkZyaRndnzYpi+EAifWJFXwoETjUHDsb1R0KWrlMYNJ5zY5g5GcYx+n0Sbmf0nGngnrxhNGLmQa1vcNDo92Mwa6Uk2TJqGV9fJK6zhw/0VjEm1c/eCLBxuH+/vLefwqSb+6xvnsbWwltc3FnLkVBMZyXGYNYEmBE63D7vVxLAEK0PiLWj+ckGbN3/tlxU0OD3cvWACf8gt4oZlm7jlwjHEmU043F5Kah2kJthIT7Lh9enUtrgZlmil1aOzr6yBTUerSLFb+ONdF3F5uxt7os3Msapm3t1RimynM10av4uut5V5fMaswqo95bR6fHzrorGMGxaP1Ry4ro0d5+IsJsz+GZjcY9V8uL8t/aBZE0wfmcxrt89lsf+mFC5D463sLWvg2TX5ZCTZOizcLK11UlLrwGbRyM5INLz8mobbp3PgRANbi2oZPyyefWUNeHVJzvAkrps5guHJcfikxKdLGls9rNxVxoUThhJvNRNvNfPZYwv9ObD7YT2DX65vbymm2eWlxW3kALZbTcRbTRRWtbCzuI5nb5rJdTNH8PKGYzy/9jBXTsnArAnMJq2DgSMlHK1sQpd0WAC8aGoGb20+zlu5RditpmDaM2OHQMPzrglBfkUTJs0YCFpMAo9P0uD0sHr/SZBw1/wJ3HvFxG7PJy3BwrKlk3h0VQEbCxqYPz45bIMY4PqcFEqdFn6z7giHTzVyVU4mUkqjT5AgkUhp9BGBczBp0Oj0sresnoykODKTbUaf7jbymtutJtxenepm44aeYrdgM5vw6DpOt4/8iibMmmDayGQEhrFW5/Dwv7vKKKtzsnT2KC7JGkZWegIXjO+aeSRnuNFfvrejjNoWNz5d0urxsaWwhuIaB0lxZqaPTGF4Shx2i4n8ikZW7z/JfQsnUt3sYsXWElZsLenyuTfPHc3TX59Bi8tHUXUeb20+zrQRybx114Xc9dZ2vvPHHSycks7h8pYePcVbi2pYudOOwPDCF1a1MGpo98b7td3MAsSKQDjej/9+gD9vK2Hx1EzibeZgHGrgWtT9fwPPvbrRF8VZTGhCUFjdzIgUO2ZNBAfpnxw8xciUOG6aM7rb77957mje2FjIE6sOsPbLCiTG7G97x0BWegLZGYk0tXrZXFDDxPQEvj57FFazxl+3l7JgUhqjhtj5zmVZrM+v5Lvv7Aq+d/HUDMakxmM1aZhNArOmYTVrmDWBxV8mAISg0enBp0v/PaTtNww806Vk5c4yth83wgfjLMamaCZNcOsbecG2a3R6KKtzMn5YPH/ZXkqzy8uIlDgmZSQyeqidofFWTJrRh5mEwOPTjf7G5aWisZVNR6vJSkvg7gUTWJ5bxOp9J7u0W2qClbnjhvLUB4dw+3SEgGkjkkmOs2A2CbYU1DB6qJ2l02M7KAAQvbn1hRDLgDVSyg+FEN8E7FLKN6M45h7gHoCxY8fOLS4uDvl9JSUluN2ReWesViul7nieXZNPeX0rNS2usPJPjh5qZ83Dl5NoM6PrkvIGJ8erHWwuqObmC8Z066HoC79bf5Rfr20zvq+ensnLt80NilRKSaPTiy4lKXZLSGMr0jayWq2MHdsx/KKp1cNzHx9mxdaSHkfRmoDJmUlBgzIpzszooXaOVDTz7fnjI+rUbnhxEwdONDI5M5FV/7Gg1+wO3RHO+VutVuJTM7nzD9s4XNEUcUzZirsvZv6knr3zj7y7h7/tOoHVrLHjJ4u7eAsi+Z0Cv9Ftv88j91jXGDQjflnvoGurWePOeeNYe/AUxTVGDOeoIXae/Op0Fk/LpN7h5tk1+WwrqqXB6cWr6+i6xG414XD5eoztFQIeWTyZBxZls62olsfe20tJbVucaFqijQanOxhTHTBqAMYPi2f+pDQeXJRNZqcB00//cYC380Jf+6GIt5q4MieDeIuJlbvKer2uNQGPfmUKt188jiaXh8zkuKjj1F/fWMCyT4/R6vF10Y/dYmJsajwtbi9ldc4O/0tLtHJZdjqF1S3MHJXMtBEpvLujNGQ84NxxQ3nm6zOZMjyywWE0/eTBKjc/WmPcxKwmjQSbkT0lEJtn1gRX5mTw6u1GfxTub5WRZCP3B1cF2/nAiQZueW1Lr5vQZCTZ0ITA4fbi8Ul/+JDGwinpPLw4O7gDYm/n7PbqSDoOUsPBarUyYtRoXt1QwEsbjkW09mBkShx1Dk8wJWNn2l8P7RmWYMXj04M7LAaYOiKZJ/7PtGAcak/c8uoWth3vmEVoeHIcM0al0OB0c+BEY4dUkXfMG8fj1+TQ4vLy990nAJg9dginGl1UNbnIGZ7ERRNSgwOxQL9x28XjmDEqhcZWD89+lM/Wolp8Xg+XjU/kjjkd+0ar1crTGypZn1/Z4VpJsVt4aFE2dy2Y0Ot5RaPpnrBarYwZM4blXxRRVudk45EqCqNMS5rUbi1EIH3cyCF2fnzd1OB6ie7YXFDNE6u+pMXlxeXVuWhCKt+8aCxen87B8kb2nWiguKYFr0+yZHom6w9VcrTSWDRq1gSv3zGXq3KM7/D6dD4/UoXNbGJHcS0rtpbQ6vbh0XU8Ptlnj3haopV7Ls9iRIqdL45WM3l4EjNGJvPYyr1UN7lxenzYLSaGp8RRVN3CRRNSuXHWKLYU1lBS00JpndMwvqUM9tWaMNKNJljNJMaZuW7mCO5bOJE4i4ljlc3sLqnDbBJMSk/i8Kkm9Hbrk+56aztX5WRgM2vsLWvA4fbicPu4cHwq91yehbexKixbYOzYsQghdkopL+itDcIxipcDy6SUe4UQXwHmSCl/Fekx7bngggvkjh07eqtb1Hj9IxO3V+8xR21aoi1qwyxaAtMTgRCK0UO73/DidODy+nC6fTg9Prw+6fcaEvRSJtrMwQVgfSWQkzLBZuo1NCGWeH069U4PDpcv5NRf5zKb2RTWQkufbnjSE6zmiMJ2esLj06l3eIJeqsDgKN5qxqfL4IDPrAkSbGbiLCa8Pp2aFjfxVlPYeXjB+O2NVFoEv0tieA6GJVq7bHPtdPto9Rhe5sD3trh8aJqhk8ZWw9jq6Zry6ZLyeifCrzHNv6lLYHOXYJlm3HzslrZUTS6vj1aPjsdnPHQJiVYzrV7DaDVrArvV1O1UZrRIKalt6TgASE2wBuvl9el4dWls+GLSsJlDz07VtbhpcXsxaYYHxaR1/JzTgZSGNzYprm2K1qdLHG4v8VZzJ0+wNPoFXeL1Sbz+Nm+PJiDZbumSFUfXJbUOd3CFeOAUk+MsSAxDNjUh9ikvo6Wx1UNDu/hx4dekCDzH6A+9usRqMmZspJQ43Eb7JFhNuP27s5n9izQDnm+X14fFZBj8Q+Mt6BJqWlzB2ZmkOEtEuVYDjpMGpwezyfAIDktoy5ak65JWf79u1rSY9U3h4HT7gnn+hYCRQ+wxWW8RCwLt5vL5groMXIta4Jo0tV2bgVk1t08nLdFKk8uLwOjr+vOalVLi8hp9XOdrsjd0XeLRdbw+Y9Mqrx6Y7ZAk2SxomjHzGJiZM76v7f3p7WbEuqublMbMaIur51R6gZnAQP8+0MTSKP4t8GcpZZ4/TCJHSvlMpMe0p7+NYoVCoVAoFAqFAsI3isMZnu4EFvifnw8cj/IYhUKhUCgUCoXijCScefF/AJuEECOBa4FvCiGellL+pIdjLol9VRUKhUKhUCgUiv6hV0+xlLIRWAjkAVdKKfd2MohDHdO3LVwUCoVCoVAoFIrTSFgrqKSUdcC7fT1GoVAoFAqFQqE4EzkndrRTKBQKhUKhUCj6Qq/ZJ/rlS4WoAsJPVho5aUB1P37+uYpqt+hQ7RY9qu2iQ7VbdKh2ix7VdtGh2i06Yt1u46SU6b0dNCBGcX8jhNgRTuoNRUdUu0WHarfoUW0XHardokO1W/SotosO1W7RMVDtpsInFAqFQqFQKBSDHmUUKxQKhUKhUCgGPeeqUfz6QFfgLEW1W3Sodose1XbRodotOlS7RY9qu+hQ7RYdA9Ju52RMsUKhUCgUCoVCEQnnqqdYoVAoFAqFQqEIG2UUDyKEEJlCiE3+53OEEOuEELlCiEf9ZaOEEGVCiA3+R7oQwiyEKGlXNnNgz0JxNtGb5tod974QYpb/eRcdDkTdFWcfYfRxT7bTVb4Q4odKb4q+EIbmsoQQnwoh9gghfuovU5o7U5FSnnUPIBPY5H8+B1gH5AKP+stGAWXABv8j3V++HNgC/GSgz2EA2mwosAbY5X+dC4wBBLAZmAAsBf690/vmAM8OdP0HuO161Fu7494HZvmfW/yvc4G7BvocBqjdetWcv/w24L/bva+LDgfbI4w+7sl2/Vs+8MPBrrlw9dbu+JX+e8Wg15u/PXrTXBbwKbAH+Km/TGmu9/vqC8B8//+/ANKV5sLSW6iyftfbWecpFkIMBf4HSPAXvQh8G1gA3CSEmABcDPynlHKh/1ElhFgKmKSU84AsIUT2QNR/APEB/wI0+l+nSilLpaG0GiAZuAS4WwixSwjxjP+4S4AbhBDbhBDLhRBhbQ1+rhCm3hBC3AYUSCn3+I97ANgppZwPfEMIkXR6a35G0KvmhBCpwPNAnRDiSv9xoXQ4aAhHc1LKJwL9G3AA+CNKc+H0cQAIIS4EyqSUJxjkeoOw+7n7gZ9JKWcBV/u9m0pzvWuuBjhPCJEJ2IB6BrnmwtRbqLJ+19tZZxQTvXG3EHjX/3wtRkMPGqSUjVLKhnZFuUKI+4UQtwLjgX3ARxjtdCEwTwhxHrAdWCylvAhjlHbdaa34wBOtYbeQNr1tBAZd8vYwNff/gPeA14A7hBBfJbQOBxPRGncLGcSaC1NvAR7CuOmC0htEb9wtRGmuN82twbBJHgTWA16U5sLRW6iyhfSz3s46r5+UshFACBEoyhVC3A/U0ibCVOApwAGs8wsuATjhf08thmt+MHMvcCXwC4zwCCmE2CyldAEIIXYD2cAHgTJgh79s0BCm3n5Bm2H3S//otbPeMk9frc9YQmluNvCYlLJCCPEusAT4YQgd7uvuQ881wtRcgIeAJ/zPleY60kVvAEKIIUCGlLLAf1yofm/Q6A3C1pwZw7AbTZtxpzTXkVB93A+AW/zPl2H0cZ8PZs2FqbdQZf2ut7PRU9yZezFi6u6nrePbLKVsklL6gIDgmgG7/z2JnBvnHjX+tjnsf7nC//djIcQIIUQ88BWMadm3hRDnCyFMwI3A3tNf2zOKUHqbDbwkpazAGMUuROmtC91o7hhGrCIYo/5iQutwMBNKc6GMO6W5dnSjN4CvAR+2e6301pVQmvsB8G9Syh9j6GwJSnMd6EZzE4AxQog4DGecRGmuM6H0Fqqs3/V21gs4AuNuJ20hE+cDx09nPc9QngYeD9xkMRbvfAbkAa9KKQ9jjHjfxlhcsUVKuW5AanqGEIFhp/QWms6a+y/gfiFELnA58AdC63DQEoFxpzTXlc56A7gaY+o1gNJbJyIw7pTmutJZc09gLIitAkoxvOxKc+0IpbduNNjvejtrN+8QQmzwLzJBCPE/wO+llIG0KFcCrwBu4HUp5e+EEMnAJozVs9cCl3SKBVIouqUXvY0Efg+kYITsLMUI4fkQY/XspRh68w1A1RVnKT1pzl/2J+DXUspd/tfjUJpT9IFe+rnrMeKw04EPgNsxQimU5hRREUYf11mD/d7HnbVGcTT4VzwuATb6p7oVin7DbywvAD5WAzDF6UBpTnG6UZpTnE76W2+DyihWKBQKhUKhUChCcdbHFCsUCoVCoVAoFH1FGcUKhUKhUCgUikGPMooVCoVCoVAoFIMeZRQrFAqFQqFQKAY9yihWKBQKhUKhUAx6/j8nfjLQqdBJPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,3))\n",
    "\n",
    "ax.plot(res_filardo.smoothed_marginal_probabilities[0])\n",
    "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='gray', alpha=0.2)\n",
    "ax.set_xlim(dta_filardo.index[6], dta_filardo.index[-1])\n",
    "ax.set(title='Smoothed probability of a low-production state');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the time-varying transition probabilities, we can see how the expected duration of a low-production state changes over time:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_filardo.expected_durations[0].plot(\n",
    "    title='Expected duration of a low-production state', figsize=(12,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During recessions, the expected duration of a low-production state is much higher than in an expansion."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
